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Journal articles on the topic 'Sharp solution'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Zhang, C. Y., Y. W. Zhang, K. Y. Zeng, and L. Shen. "Nanoindentation of Polymers with a Sharp Indenter." Journal of Materials Research 20, no. 6 (2005): 1597–605. http://dx.doi.org/10.1557/jmr.2005.0200.

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A five-step indentation scheme is proposed to extract the elastic and viscoelastic properties of polymeric materials using a sharp indenter. In the formulation, analytical solutions to the elastic-viscoelastic deformation based on the concept of “effective indenters” proposed by both Pharr and Bolshakov [Understanding nanoindentation unloading curves. J. Mater. Res.17, 2660 (2002)] and Sakai [Elastic recovery in the unloading process of pyramidal microindentation. J. Mater. Res.18, 1631 (2003)] were derived. Indentation experiments on polymethylmethacrylate following the five-step scheme were

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Li, Si-Huan, Qiang Wang, Shu Xu, and Jun-Xiang Wang. "Sharp Efficiency for Vector Equilibrium Problems on Banach Spaces." Abstract and Applied Analysis 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/128178.

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The concept of sharp efficient solution for vector equilibrium problems on Banach spaces is proposed. Moreover, the Fermat rules for local efficient solutions of vector equilibrium problems are extended to the sharp efficient solutions by means of the Clarke generalized differentiation and the normal cone. As applications, some necessary optimality conditions and sufficient optimality conditions for local sharp efficient solutions of a vector optimization problem with an abstract constraint and a vector variational inequality are obtained, respectively.

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GOLOVIZNIN, V. V., and T. J. SCHEP. "Self-induced transparency in plasmas with sharp boundary." Laser and Particle Beams 18, no. 3 (2000): 361–65. http://dx.doi.org/10.1017/s0263034600183028.

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We study fully relativistic nonlinear 1D fluid equations describing steady-state solutions for an electromagnetic wave interacting with plasma in the self-induced transparency regime. In addition to the well-known solution that corresponds to the transmission of the electromagnetic wave into plasma, another steady-state solution is shown to exist in a certain range of the amplitude of the wave. The latter one satisfies the same boundary conditions but corresponds to the full reflection of the incident wave. The co-existence of the two solutions indicates a rich structure of the interface betwe

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Work, Dalon, Oisin Tong, Ryan Workman, Aaron Katz, and Andrew M. Wissink. "Strand-Grid-Solution Procedures for Sharp Corners." AIAA Journal 52, no. 7 (2014): 1528–41. http://dx.doi.org/10.2514/1.j052607.

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Ankudinov, A. L. "Hypersonic Nonequilibrium Flow around Sharp Edge." Прикладная математика и механика 87, no. 1 (2023): 26–35. http://dx.doi.org/10.31857/s0032823523010034.

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A regularized problem has been formulated to describe the flow of a molecular gas in a hypersonic macrokinetic nonequilibrium thin viscous shock layer (kinetic TVSL) near a sharp edge. It is shown that the solution of the regularized kinetic TVSL problem on the sharp edge, the description of friction and heat transfer coincides with the solution of the Navier–Stokes analogue of this TVSL problem. It is shown that in the kinetic TVSL the friction stress and the normal heat flow on the wall in the vicinity of the sharp edge are identical with the corresponding values in the Navier–Stokes TVSL. T

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6

Malakhov, A. N. "Diffusion through sharp potential barriers I. Exact solution." Radiophysics and Quantum Electronics 34, no. 5 (1991): 451–60. http://dx.doi.org/10.1007/bf01036839.

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7

LEONARD, B. P., and SIMIN MOKHTARI. "ULTRA‐SHARP SOLUTION OF THE SMITH‐HUTTON PROBLEM." International Journal of Numerical Methods for Heat & Fluid Flow 2, no. 5 (1992): 407–27. http://dx.doi.org/10.1108/eb017502.

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Rathore, Uma, S.N. Jatolia, S. K. Verma, and Singh Ranveer. "Spectral Properties and Applications of Ln (III) Ion and Their Complexes." Pharmaceutical and Chemical Journal 1, no. 3 (2014): 40–43. https://doi.org/10.5281/zenodo.13692077.

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In lanthanides transitions involve only a redistribution of electrons within the 4f-orbitals (f↔f transition) are orbitally forbidden by the selection rule. Crystal field effects in lanthanides are virtually insignificant due to 4f-electrons are well shielded from external charge by 5s<sup>2</sup> and 5p<sup>6</sup> sub-shells.  Their (f↔f transition) absorption bands are very sharp. Their optical spectra are virtually independent of environment they show similar spectra in gas/solution/solid (sharp lines like typical gas atom spectra).  Analysis of the UV-Visible spectra f

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9

Thandapani, E. "A sharp upper bound for discrete inequalities of Gronwall-Bellman type." Journal of Applied Mathematics and Simulation 2, no. 2 (1989): 113–16. http://dx.doi.org/10.1155/s1048953389000092.

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A sharp upper bound is given for solutions of a discrete inequality of the Gronwall-Bellman type. The bound, which is the exact solution of the corresponding discrete equation, is obtained by reducing the equation to a system of difference equations.

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10

KERDKAEW, JUTAMAS, RABIAN WANGKEEREE, and GUE MYUNG LEE. "On optimality conditions for robust weak sharp solution in uncertain optimizations." Carpathian Journal of Mathematics 36, no. 3 (2020): 443–52. http://dx.doi.org/10.37193/cjm.2020.03.12.

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In this paper, we investigate the robust optimization problem involving nonsmooth and nonconvex real-valued functions. We firstly establish a necessary condition for the local robust weak sharp solution of considered problem under a constraint qualification. These optimality conditions are presented in terms of multipliers and Mordukhovich subdifferentials of the related functions. Then, by employing the robust version of the (KKT) condition, and some appropriate generalized convexity conditions, we also obtain some sufficient conditions for the global robust weak sharp solutions of the proble

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11

Choi, Woocheol, and Young-Pil Choi. "A sharp error analysis for the DG method of optimal control problems." AIMS Mathematics 7, no. 5 (2022): 9117–55. http://dx.doi.org/10.3934/math.2022506.

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<abstract><p>In this paper, we are concerned with a nonlinear optimal control problem of ordinary differential equations. We consider a discretization of the problem with the discontinuous Galerkin method with arbitrary order $ r \in \mathbb{N}\cup \{0\} $. Under suitable regularity assumptions on the cost functional and solutions of the state equations, we first show the existence of a local solution to the discretized problem. We then provide sharp estimates for the $ L^2 $-error of the approximate solutions. The convergence rate of the error depends on the regularity of the opti

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Song, T., K. Upreti, and G. Subbarayan. "A sharp interface isogeometric solution to the Stefan problem." Computer Methods in Applied Mechanics and Engineering 284 (February 2015): 556–82. http://dx.doi.org/10.1016/j.cma.2014.10.013.

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13

Ron, Alon, Amir Hevroni, Eran Maniv, et al. "Solution Monolayer Epitaxy for Tunable Atomically Sharp Oxide Interfaces." Advanced Materials Interfaces 4, no. 22 (2017): 1700688. http://dx.doi.org/10.1002/admi.201700688.

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Fino, Anna, Gueo Grantcharov, and Luigi Vezzoni. "Solutions to the Hull–Strominger System with Torus Symmetry." Communications in Mathematical Physics 388, no. 2 (2021): 947–67. http://dx.doi.org/10.1007/s00220-021-04223-7.

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AbstractWe construct new smooth solutions to the Hull–Strominger system, showing that the Fu–Yau solution on torus bundles over K3 surfaces can be generalized to torus bundles over K3 orbifolds. In particular, we prove that, for $$13 \le k \le 22$$ 13 ≤ k ≤ 22 and $$14\le r\le 22$$ 14 ≤ r ≤ 22 , the smooth manifolds $$S^1\times \sharp _k(S^2\times S^3)$$ S 1 × ♯ k ( S 2 × S 3 ) and $$\sharp _r (S^2 \times S^4) \sharp _{r+1} (S^3 \times S^3)$$ ♯ r ( S 2 × S 4 ) ♯ r + 1 ( S 3 × S 3 ) , have a complex structure with trivial canonical bundle and admit a solution to the Hull–Strominger system.

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Kamalinejad, Ehsan, and Amir Moradifam. "Radial symmetry of large solutions of semilinear elliptic equations with convection." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 144, no. 1 (2014): 139–47. http://dx.doi.org/10.1017/s0308210512001229.

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We study the radial symmetry of large solutions of the semilinear elliptic problem Δu + ∇h · ∇u = f (∣x∣, u), and we provide sharp conditions under which the problem has a radial solution. The result is independent of the rate of growth of the solution at infinity.

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Navarro, Miguel Angel, and Justino Sánchez. "Sharp estimates of semistable radial solutions of k-Hessian equations." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 4 (2019): 2083–115. http://dx.doi.org/10.1017/prm.2019.14.

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AbstractWe consider semistable, radially symmetric and increasing solutions of Sk(D2u) = g(u) in the unit ball of ℝn, where Sk(D2u) is the k-Hessian operator of u and g ∈ C1 is a general positive nonlinearity. We establish sharp pointwise estimates for such solutions in a proper weighted Sobolev space, which are optimal and do not depend on the specific nonlinearity g. As an application of these results, we obtain pointwise estimates for the extremal solution and its derivatives (up to order three) of the equation Sk(D2u) = λg(u), posed in B1, with Dirichlet data $u\arrowvert _{B_1}=0$, where

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17

Izmailova, Yulia, Ilia Marchevsky, and Kseniia Sokol. "Singularity resolving in solution of the boundary integral equation in two-dimensional vortex methods." Journal of Physics: Conference Series 2543, no. 1 (2023): 012002. http://dx.doi.org/10.1088/1742-6596/2543/1/012002.

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Abstract The problem of 2D incompressible flow simulation around airfoils with sharp edges and corner point is considered. The solution of the boundary integral equation with respect to vortex sheet intensity arising in Lagrangian vortex method has weak singularity that cannot be resolved correctly in the framework of the existing Galerkin-type numerical schemes. It is shown that for piecewise-smooth bounded solutions the known schemes allow for solution reconstruction with high quality and provide the 2-nd order of accuracy, while for singular solution their order of accuracy goes down to the

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18

Wang, Liqun, Songming Hou, and Liwei Shi. "A Numerical Method for Solving 3D Elasticity Equations with Sharp-Edged Interfaces." International Journal of Partial Differential Equations 2013 (July 21, 2013): 1–13. http://dx.doi.org/10.1155/2013/476873.

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Interface problems occur frequently when two or more materials meet. Solving elasticity equations with sharp-edged interfaces in three dimensions is a very complicated and challenging problem for most existing methods. There are several difficulties: the coupled elliptic system, the matrix coefficients, the sharp-edged interface, and three dimensions. An accurate and efficient method is desired. In this paper, an efficient nontraditional finite element method with nonbody-fitting grids is proposed to solve elasticity equations with sharp-edged interfaces in three dimensions. The main idea is t

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Fu, Xiaoming, Quentin Griette, and Pierre Magal. "Sharp discontinuous traveling waves in a hyperbolic Keller–Segel equation." Mathematical Models and Methods in Applied Sciences 31, no. 05 (2021): 861–905. http://dx.doi.org/10.1142/s0218202521500214.

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In this work, we describe a hyperbolic model with cell–cell repulsion with a dynamics in the population of cells. More precisely, we consider a population of cells producing a field (which we call “pressure”) which induces a motion of the cells following the opposite of the gradient. The field indicates the local density of population and we assume that cells try to avoid crowded areas and prefer locally empty spaces which are far away from the carrying capacity. We analyze the well-posedness property of the associated Cauchy problem on the real line. We start from bounded initial conditions a

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20

Chen, Kuangshi, Jinglei Xu, Qihao Qin, and Shuai Huang. "Analytical solution of supersonic axisymmetric flow around a sharp convex corner." Physics of Fluids 35, no. 1 (2023): 016118. http://dx.doi.org/10.1063/5.0134698.

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Supersonic axisymmetric expansion flow is a typical and fundamental issue in gas dynamics. It plays a vital role in the high-speed external and internal flow fields regarding the contour design and performance evaluation of supersonic/hypersonic vehicles and their propulsion systems. The supersonic two-dimensional (2D) planar expansion flow is dominated by the well-known Prandtl–Meyer (P–M) theory. However, no similar explicit relation exists for the supersonic axisymmetric expansion flow, and only the computational fluid dynamics results could be employed at present. Therefore, this work focu

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21

Chaudhuri, Sid. "The problem of a hydrogen atom in a cavity: Oscillator representation solution versus analytic solution." Open Physics 19, no. 1 (2021): 61–68. http://dx.doi.org/10.1515/phys-2021-0201.

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Abstract A solution to the problem of a hydrogenic atom in a homogeneous dielectric medium with a concentric spherical cavity using the oscillator representation method (ORM) is presented. The results obtained by the ORM are compared with a known exact analytic solution. The energy levels of the hydrogenic atom in a spherical cavity exhibit a shallow-deep instability as a function of the cavity radius. The sharpness of the transition depends on the value of the dielectric constant of the medium. The results of the ORM agree well with the results obtained by the analytic solution when the shall

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22

ZURER, PAMELA S. "Researchers Seek Solution to Sharp Drop in NIH Research Grants." Chemical & Engineering News 68, no. 29 (1990): 20–21. http://dx.doi.org/10.1021/cen-v068n029.p020.

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23

Myers, T. G. "A series solution method for sharp asymmetric dry contact problems." Journal of Strain Analysis for Engineering Design 26, no. 1 (1991): 39–45. http://dx.doi.org/10.1243/03093247v261039.

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24

Ono, Kosuke. "On global existence and asymptotic stability of solutions of mildly degenerate dissipative nonlinear wave equations of Kirchhoff type." Asymptotic Analysis 16, no. 3-4 (1998): 299–314. https://doi.org/10.3233/asy-1998-287.

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We consider the global existence and asymptotic stability of solutions to the Cauchy problem for degenerate nonlinear wave equations of Kirchhoff type with a dissipative term in unbounded domain. We derive the sharp decay estimates of the solution and its derivatives. Moreover, we show that the solution has a lower decay estimate of some algebraic rate.

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25

Mohammed, Ahmed, and Giovanni Porru. "A sharp global estimate and an overdetermined problem for Monge-Ampère type equations." Advanced Nonlinear Studies 22, no. 1 (2022): 1–14. http://dx.doi.org/10.1515/ans-2022-0001.

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Abstract We consider Monge-Ampère type equations involving the gradient that are elliptic in the framework of convex functions. Through suitable symmetrization we find sharp estimates to solutions of such equations. An overdetermined problem related to our Monge-Ampère type operators is also considered and we show that such a problem may admit a solution only when the underlying domain is a ball.

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26

Pavlov, S. Kh. "PROCESSES OF FORMATION OF SODIUM BICARBONATE GROUNDWATER IN THE RAINWATER – SANDSTONE SYSTEM." Geodynamics & Tectonophysics 14, no. 6 (2023): 0733. http://dx.doi.org/10.5800/gt-2023-14-6-0733.

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In modeling, a study was made of the processes of the physical-chemical interaction between rainwater and sandstone. It was stated that as a result of the interaction, already in mineralization of water equal to 55 mg/l, there emerges a pure soda solution whose sharp oxidation properties, retaining up to 200 mg/l, change to sharp restorative when exceeding this value. At the mineralization of water equal to 30 mg/l, an intensive increase in the number of hydroxide ions in a solution makes it highly alkaline. The active removal of calcium from solution is due to the formation of not only solid

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Zhu, Xiaoli, Fuyi Li, and Yuhua Li. "Some sharp results about the global existence and blowup of solutions to a class of pseudo-parabolic equations." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 147, no. 6 (2017): 1311–31. http://dx.doi.org/10.1017/s0308210516000494.

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In this paper we are interested in a sharp result about the global existence and blowup of solutions to a class of pseudo-parabolic equations. First, we represent a unique local weak solution in a new integral form that does not depend on any semigroup. Second, with the help of the Nehari manifold related to the stationary equation, we separate the whole space into two components S+ and S– via a new method, then a sufficient and necessary condition under which the weak solution blows up is established, that is, a weak solution blows up at a finite time if and only if the initial data belongs t

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Wang, Ruyu, Wenling Zhao, Daojin Song, and Yaozhong Hu. "The Augmented Weak Sharpness of Solution Sets in Equilibrium Problems." Mathematics 12, no. 2 (2024): 352. http://dx.doi.org/10.3390/math12020352.

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This study considers equilibrium problems, focusing on identifying finite solutions for feasible solution sequences. We introduce an innovative extension of the weak sharp minimum concept from convex programming to equilibrium problems, coining this as weak sharpness for solution sets. Recognizing situations where the solution set may not exhibit weak sharpness, we propose an augmented mapping approach to mitigate this limitation. The core of our research is the formulation of augmented weak sharpness for the solution set. This comprehensive concept encapsulates both weak sharpness and strong

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Istrate, Gabriel. "Satisfying Assignments of Random Boolean Constraint Satisfaction Problems: Clusters and Overlaps." JUCS - Journal of Universal Computer Science 13, no. (11) (2007): 1655–70. https://doi.org/10.3217/jucs-013-11-1655.

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The distribution of overlaps of solutions of a random constraint satisfaction problem (CSP) is an indicator of the overall geometry of its solution space. For random k-SAT, nonrigorous methods from Statistical Physics support the validity of the one step replica symmetry breaking approach. Some of these predictions were rigorously confirmed in [Mézard et al. 2005a] [Mézard et al. 2005b]. There it is proved that the overlap distribution of random k-SAT, k ≥ 9, has discontinuous support. Furthermore, Achlioptas and Ricci-Tersenghi [Achlioptas and Ricci-Tersenghi 2006] proved that, for random k-S

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Liao, Boshu, and Mustafa M. Aral. "Semi-analytical solution of two-dimensional sharp interface LNAPL transport models." Journal of Contaminant Hydrology 44, no. 3-4 (2000): 203–21. http://dx.doi.org/10.1016/s0169-7722(00)00104-2.

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31

GUO, ZONGMING, and J. R. L. WEBB. "PROFILE OF SOLUTIONS WITH SHARP LAYERS TO SOME SINGULARLY PERTURBED QUASILINEAR DIRICHLET PROBLEMS." Communications in Contemporary Mathematics 05, no. 06 (2003): 883–920. http://dx.doi.org/10.1142/s021919970300118x.

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The singularly perturbed problem for the p-Laplacian [Formula: see text] is studied in a convex bounded domain Ω containing 0 when p > 2, f(0) = 0 and f has precisely 3 positive zeros. There exist a small solution [Formula: see text] and a large solution [Formula: see text] when ε is sufficiently small. By using the mountain pass lemma we show there is an intermediate positive solution uε and we study the structure of this solution.

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Jančič, Mitja, Miha Založnik, and Gregor Kosec. "A sharp-interface mesoscopic model for dendritic growth." IOP Conference Series: Materials Science and Engineering 1274, no. 1 (2023): 012046. http://dx.doi.org/10.1088/1757-899x/1274/1/012046.

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Abstract The grain envelope model (GEM) describes the growth of envelopes of dendritic crystal grains during solidification. Numerically the growing envelopes are usually tracked using an interface capturing method employing a phase field equation on a fixed grid. Such an approach describes the envelope as a diffuse interface, which can lead to numerical artefacts that are possibly detrimental. In this work, we present a sharp-interface formulation of the GEM that eliminates such artefacts and can thus track the envelope with high accuracy. The new formulation uses an adaptive meshless discret

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Thrasher, W. John, and Michael Mascagni. "Examining sharp restart in a Monte Carlo method for the linearized Poisson–Boltzmann equation." Monte Carlo Methods and Applications 26, no. 3 (2020): 223–44. http://dx.doi.org/10.1515/mcma-2020-2069.

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AbstractIt has been shown that when using a Monte Carlo algorithm to estimate the electrostatic free energy of a biomolecule in a solution, individual random walks can become entrapped in the geometry. We examine a proposed solution, using a sharp restart during the Walk-on-Subdomains step, in more detail. We show that the point at which this solution introduces significant bias is related to properties intrinsic to the molecule being examined. We also examine two potential methods of generating a sharp restart point and show that they both cause no significant bias in the examined molecules a

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LIU, YONGQIN, and SHUICHI KAWASHIMA. "DECAY PROPERTY FOR THE TIMOSHENKO SYSTEM WITH MEMORY-TYPE DISSIPATION." Mathematical Models and Methods in Applied Sciences 22, no. 02 (2012): 1150012. http://dx.doi.org/10.1142/s0218202511500126.

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In this paper we consider the initial value problem for the Timoshenko system with a memory term. We construct the fundamental solution by using the Fourier–Laplace transform and obtain the solution formula of the problem. Moreover, applying the energy method in the Fourier space, we derive the pointwise estimate of solutions in the Fourier space, which gives a sharp decay estimate of solutions. It is shown that the decay property of the system is of the regularity-loss type and is weaker than that of the Timoshenko system with a frictional dissipation.

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Mao, Zhiping, and Xuhui Meng. "Physics-informed neural networks with residual/gradient-based adaptive sampling methods for solving partial differential equations with sharp solutions." Applied Mathematics and Mechanics 44, no. 7 (2023): 1069–84. http://dx.doi.org/10.1007/s10483-023-2994-7.

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AbstractWe consider solving the forward and inverse partial differential equations (PDEs) which have sharp solutions with physics-informed neural networks (PINNs) in this work. In particular, to better capture the sharpness of the solution, we propose the adaptive sampling methods (ASMs) based on the residual and the gradient of the solution. We first present a residual only-based ASM denoted by ASM I. In this approach, we first train the neural network using a small number of residual points and divide the computational domain into a certain number of sub-domains, then we add new residual poi

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Grassia, P., E. Mas-Hernández, N. Shokri, S. J. Cox, G. Mishuris, and W. R. Rossen. "Analysis of a model for foam improved oil recovery." Journal of Fluid Mechanics 751 (June 20, 2014): 346–405. http://dx.doi.org/10.1017/jfm.2014.287.

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AbstractDuring improved oil recovery (IOR), gas may be introduced into a porous reservoir filled with surfactant solution in order to form foam. A model for the evolution of the resulting foam front known as ‘pressure-driven growth’ is analysed. An asymptotic solution of this model for long times is derived that shows that foam can propagate indefinitely into the reservoir without gravity override. Moreover, ‘pressure-driven growth’ is shown to correspond to a special case of the more general ‘viscous froth’ model. In particular, it is a singular limit of the viscous froth, corresponding to th

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Cai, Jingjing, and Quanjun Wu. "ASYMPTOTIC BEHAVIOR FOR RADIALLY SYMMETRIC SOLUTIONS OF A LOGISTIC EQUATION WITH A FREE BOUNDARY." Mathematical Modelling and Analysis 22, no. 1 (2017): 21–36. http://dx.doi.org/10.3846/13926292.2017.1258678.

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In this paper we investigate a logistic equation with a new free boundary condition appearing in ecology, we aim to describe the spreading of a new or invasive species by studying the asymptotic behavior of the radially symmetric solutions of the problem. We will obtain a trichotomy result: spreading (the solution converges to a stationary solution defined on the half–line), transition (the solution converges to a stationary solution with compact support) and vanishing (the solution converges to 0 within a finite time). Besides we can also obtain a dichotomy result (either spreading or vanishi

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Wang, Liqun, and Liwei Shi. "A Numerical Method for Solving Matrix Coefficient Heat Equations with Interfaces." Numerical Mathematics: Theory, Methods and Applications 8, no. 4 (2015): 475–95. http://dx.doi.org/10.4208/nmtma.2015.m1331.

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AbstractIn this paper, we propose a numerical method for solving the heat equations with interfaces. This method uses the non-traditional finite element method together with finite difference method to get solutions with second-order accuracy. It is capable of dealing with matrix coefficient involving time, and the interfaces under consideration are sharp-edged interfaces instead of smooth interfaces. Modified Euler Method is employed to ensure the accuracy in time. More than 1.5th order accuracy is observed for solution with singularity (second derivative blows up) on the sharp-edged interfac

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Kozlov, Vladimir, and Vladimir Maz'ya. "Sharp conditions for the classical asymptotic behaviour near a point for solutions to quasilinear elliptic systems." Asymptotic Analysis 38, no. 2 (2004): 143–65. https://doi.org/10.3233/asy-2004-616.

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It is well known that distributional solutions of an elliptic equation with constant coefficients behave asymptotically near an interior point as sums of polynomials and linear combinations of derivatives of a fundamental solution. We consider a class of quasilinear elliptic systems and give mild conditions ensuring the same asymptotic behaviour. The sharpness of our conditions is illustrated by examples. The results are obtained as corollaries of a general theorem on the asymptotics of solutions to nonlinear ordinary differential equations in Banach spaces.

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Jin, Fabian, Samuel Lanthaler, Milton da Costa Lopes Filho, and Helena Judith Nussenzveig Lopes. "Sharp conditions for energy balance in two-dimensional incompressible ideal flow with external force." Nonlinearity 38, no. 7 (2025): 075007. https://doi.org/10.1088/1361-6544/add4b6.

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Abstract Smooth solutions of the forced incompressible Euler equations satisfy an energy balance, where the rate-of-change in time of the kinetic energy equals the work done by the force per unit time. Interesting phenomena such as turbulence are closely linked with rough solutions which may exhibit inviscid dissipation, or, in other words, for which energy balance does not hold. This article provides a characterization of energy balance for physically realizable weak solutions of the forced incompressible Euler equations, i.e. solutions which are obtained in the limit of vanishing viscosity.

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Wang, Xu, Ping Yang, and Peter Schiavone. "Interaction of a screw dislocation with a parabolic cavity and a semi-infinite crack." Mathematics and Mechanics of Solids 25, no. 10 (2020): 1896–903. http://dx.doi.org/10.1177/1081286520914698.

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We derive an analytic solution to the problem of a screw dislocation interacting with a parabolic cavity and a semi-infinite sharp crack using conformal mapping techniques and the method of images. Closed-form expressions for the image force acting on the screw dislocation, the mode III stress intensity factor at the crack tip and the generalized mode III stress intensity factor for the parabolic cavity are obtained. The correctness of the solution is validated by comparison with existing solutions in the literature.

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Carrillo, José A., Young-Pil Choi, and Ewelina Zatorska. "On the pressureless damped Euler–Poisson equations with quadratic confinement: Critical thresholds and large-time behavior." Mathematical Models and Methods in Applied Sciences 26, no. 12 (2016): 2311–40. http://dx.doi.org/10.1142/s0218202516500548.

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We analyze the one-dimensional pressureless Euler–Poisson equations with linear damping and nonlocal interaction forces. These equations are relevant for modeling collective behavior in mathematical biology. We provide a sharp threshold between the supercritical region with finite-time breakdown and the subcritical region with global-in-time existence of the classical solution. We derive an explicit form of solution in Lagrangian coordinates which enables us to study the time-asymptotic behavior of classical solutions with the initial data in the subcritical region.

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Dautov, Rafail Z., and Alexander V. Lapin. "Sharp error estimate for implicit finite element scheme for American put option." Russian Journal of Numerical Analysis and Mathematical Modelling 34, no. 2 (2019): 85–94. http://dx.doi.org/10.1515/rnam-2019-0007.

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AbstractWe investigate a numerical solution method for a degenerate parabolic variational inequality that determines American vanilla put pricing. This method is based on piecewise linear finite elements in spatial variables and the backward Euler finite difference in time variable. For the approximate solution, we get sharp error estimate of orderO(h+τ3/4) in the energy norm of the corresponding differential operator.

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Rajopadhye, S. V. "Decay rates for the solutions of model equations for bore propagation." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 125, no. 2 (1995): 371–98. http://dx.doi.org/10.1017/s0308210500028080.

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We study the large-time behaviour of solutions to the Korteweg-de Vries-Burgers equation with bore-like initial data. This work relies on the methods of Amick, Bona and Schonbeck to obtain sharp rates of temporal decay of certain norms of the solution, thus obtaining an improvement over results of Naumkin and Shishmarev.

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Kerdkaew, Jutamas, and Rabian Wangkeeree. "Characterizing robust weak sharp solution sets of convex optimization problems with uncertainty." Journal of Industrial & Management Optimization 16, no. 6 (2020): 2651–73. http://dx.doi.org/10.3934/jimo.2019074.

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Anastassiou, George A., and Alexander Bendikov. "A sharp error estimate for the numerical solution of multivariate dirichlet problem." Stochastic Analysis and Applications 16, no. 3 (1998): 403–22. http://dx.doi.org/10.1080/07362999808809542.

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Anastassiou, George A., and Alexander Bendikov. "A sharp error estimate for the numerical solution of multivariate Dirichlet problems." Journal of Computational and Applied Mathematics 75, no. 2 (1996): 215–29. http://dx.doi.org/10.1016/s0377-0427(96)00052-0.

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Kacimov, A. R. "Analytical solution to a sharp interface problem in a vortex-generated flow." Water Resources Research 37, no. 12 (2001): 3387–91. http://dx.doi.org/10.1029/2001wr000384.

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Viitasaari, Lauri, and Caibin Zeng. "Stationary Wong–Zakai Approximation of Fractional Brownian Motion and Stochastic Differential Equations with Noise Perturbations." Fractal and Fractional 6, no. 6 (2022): 303. http://dx.doi.org/10.3390/fractalfract6060303.

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In this article, we introduce a Wong–Zakai type stationary approximation to the fractional Brownian motions and provide a sharp rate of convergence in Lp(Ω). Our stationary approximation is suitable for all values of H∈(0,1). As an application, we consider stochastic differential equations driven by a fractional Brownian motion with H>1/2. We provide sharp rate of convergence in a certain fractional-type Sobolev space of the approximation, which in turn provides rate of convergence for the solution of the approximated equation. This generalises some existing results in the literature concer

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KARAMI, A., H. R. KARIMI, B. MOSHIRI, and P. JABEDAR MARALANI. "WAVELET-BASED ADAPTIVE COLLOCATION METHOD FOR THE RESOLUTION OF NONLINEAR PDEs." International Journal of Wavelets, Multiresolution and Information Processing 05, no. 06 (2007): 957–73. http://dx.doi.org/10.1142/s0219691307002154.

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Theoretical modeling of dynamic processes in chemical engineering often implies the numeric solution of one or more partial differential equations. The complexity of such problems is increased when the solutions exhibit sharp moving fronts. An efficient adaptive multiresolution numerical method is described for solving systems of partial differential equations. This method is based on multiresolution analysis and interpolating wavelets, that dynamically adapts the collocation grid so that higher resolution is automatically attributed to domain regions where sharp features are present. Space de

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