Relevant bibliographies by topics / Nonlinear PDE

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Nonlinear PDE'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Nonlinear PDE"

1

Yang, Lei, Jianbin Liu, and Kongqing Yang. "Exact solutions of nonlinear PDE, nonlinear transformations and reduction of nonlinear PDE to a quadrature." Physics Letters A 278, no. 5 (2001): 267–70. http://dx.doi.org/10.1016/s0375-9601(00)00778-7.

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Holcman, David. "Nonlinear PDE with vector fields." Journal d'Analyse Mathématique 81, no. 1 (2000): 111–37. http://dx.doi.org/10.1007/bf02788987.

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Moon, Minam, Hyung Kyu Jun, and Tay Suh. "Error Estimates on Hybridizable Discontinuous Galerkin Methods for Parabolic Equations with Nonlinear Coefficients." Advances in Mathematical Physics 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/9736818.

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HDG method has been widely used as an effective numerical technique to obtain physically relevant solutions for PDE. In a practical setting, PDE comes with nonlinear coefficients. Hence, it is inevitable to consider how to obtain an approximate solution for PDE with nonlinear coefficients. Research on using HDG method for PDE with nonlinear coefficients has been conducted along with results obtained from computer simulations. However, error analysis on HDG method for such settings has been limited. In this research, we give error estimations of the hybridizable discontinuous Galerkin (HDG) met
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Zhang, Zhi-Yong. "Symmetry determination and nonlinearization of a nonlinear time-fractional partial differential equation." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2233 (2020): 20190564. http://dx.doi.org/10.1098/rspa.2019.0564.

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We first show that the infinitesimal generator of Lie symmetry of a time-fractional partial differential equation (PDE) takes a unified and simple form, and then separate the Lie symmetry condition into two distinct parts, where one is a linear time-fractional PDE and the other is an integer-order PDE that dominates the leading position, even completely determining the symmetry for a particular type of time-fractional PDE. Moreover, we show that a linear time-fractional PDE always admits an infinite-dimensional Lie algebra of an infinitesimal generator, just as the case for a linear PDE and a
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Abbott, Steve, V. P. Maslov, and G. A. Omel'yanov. "Geometric Asymptotics for Nonlinear PDE I." Mathematical Gazette 86, no. 507 (2002): 574. http://dx.doi.org/10.2307/3621211.

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Ghiu, Cristian, Constantin Udriste, and Lavinia Laura Petrescu. "Families of Solutions of Multitemporal Nonlinear Schrödinger PDE." Mathematics 9, no. 16 (2021): 1995. http://dx.doi.org/10.3390/math9161995.

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The multitemporal nonlinear Schrödinger PDE (with oblique derivative) was stated for the first time in our research group as a universal amplitude equation which can be derived via a multiple scaling analysis in order to describe slow modulations of the envelope of a spatially and temporarily oscillating wave packet in space and multitime (an equation which governs the dynamics of solitons through meta-materials). Now we exploit some hypotheses in order to find important explicit families of exact solutions in all dimensions for the multitime nonlinear Schrödinger PDE with a multitemporal dire
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Ni, Xu, Kejia Yi, Yiming Jiang, Ancai Zhang, and Chengdong Yang. "Consensus Control of Leaderless and Leader-Following Coupled PDE-ODEs Modeled Multi-Agent Systems." Mathematics 10, no. 2 (2022): 201. http://dx.doi.org/10.3390/math10020201.

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This paper discusses consensus control of nonlinear coupled parabolic PDE-ODE-based multi-agent systems (PDE-ODEMASs). First, a consensus controller of leaderless PDE-ODEMASs is designed. Based on a Lyapunov-based approach, coupling strengths are obtained for leaderless PDE-ODEMASs to achieve leaderless consensus. Furthermore, a consensus controller in the leader-following PDE-ODEMAS is designed and the corresponding coupling strengths are obtained to ensure the leader-following consensus. Two examples show the effectiveness of the proposed methods.
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Costin, O., and S. Tanveer. "Complex Singularity Analysis for a Nonlinear PDE." Communications in Partial Differential Equations 31, no. 4 (2006): 593–637. http://dx.doi.org/10.1080/03605300500455941.

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Annabi, Yosra. "Nonlinear PDE in variable exponent Sobolev spaces." International Journal of Multidisciplinary Research and Growth Evaluation 5, no. 5 (2024): 252–58. http://dx.doi.org/10.54660/.ijmrge.2024.5.5.252-258.

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In this article, the author introduces the Lebesgue and Sobolev functional spaces with variable exponents. For this, she proposes a direct problem to be solved in these spaces. In addition, she presents a comparison of convergence theorems in spaces with fixed exponents and those with variable exponents.
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Kubo, Masahiro, and Quqin Lu. "Evolution equations for nonlinear degenerate parabolic PDE." Nonlinear Analysis: Theory, Methods & Applications 64, no. 8 (2006): 1849–59. http://dx.doi.org/10.1016/j.na.2005.07.027.

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Dissertations / Theses on the topic "Nonlinear PDE"

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Sabra, Ahmad. "Nonlinear PDE and Optical Surfaces Design." Diss., Temple University Libraries, 2015. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/345398.

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Mathematics<br>Ph.D.<br>We introduce two models to design near field reflectors in R^3 that solve an inverse problem in radiometry, taking into account the inverse square law of irradiance. The problem leads to a Monge-Ampere type inequality. The surfaces in the first model are strictly convex and require to be far from the source to avoid obstruction. In the second model, the reflectors are neither convex nor concave and do not block the rays even if they are close to the source.<br>Temple University--Theses
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Saha, Rupesh Kumar. "On some aspects of nonlinearity and role of parameters in some nonlinear PDE`s from physical origin." Thesis, University of North Bengal, 2009. http://hdl.handle.net/123456789/1372.

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Ching, Joshua. "Singular Solutions of Nonlinear Elliptic Equations with Gradient Terms." Thesis, The University of Sydney, 2017. http://hdl.handle.net/2123/16848.

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On punctured domains of $\mathbb{R}^N$ with $N \geq 2$, we study non-negative solutions to a nonlinear elliptic equation with a gradient term: $div(|x|^\sigma |\nabla u|^{p-2} \nabla u)=|x|^{-\tau} u^q |\nabla u|^m$ (*), where m,q>0 and 1<p\leq N. In Chapter 1, we review the literature. In Chapter 2, we completely classify the behaviour of solutions near zero for (*) where $\sigma=\tau=0$ and p=2. Suppose that 0<m<2 and m+q>1. Our classification depends on the position of q relative to a critical exponent $q_*=(N−m(N−1))/(N−2)$. We prove the following: If $q<q_*$, then any positive solution
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Sichau, Adrian [Verfasser]. "Robust Nonlinear Programming with Discretized PDE Constraints using Second-order Approximations / Adrian Sichau." München : Verlag Dr. Hut, 2014. http://d-nb.info/1055863125/34.

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Lass, Oliver [Verfasser]. "Reduced order modeling and parameter identification for coupled nonlinear PDE systems / Oliver Lass." Konstanz : Bibliothek der Universität Konstanz, 2014. http://d-nb.info/104939366X/34.

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Candy, Timothy Lars. "Local and global well-posedness for nonlinear Dirac type equations." Thesis, University of Edinburgh, 2012. http://hdl.handle.net/1842/7962.

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We investigate the local and global well-posedness of a variety of nonlinear Dirac type equations with null structure on R1+1. In particular, we prove global existence in L2 for a nonlinear Dirac equation known as the Thirring model. Local existence in Hs for s > 0, and global existence for s > 1/2 , has recently been proven by Selberg-Tesfahun where they used Xs,b spaces together with a type of null form estimate. In contrast, motivated by the recent work of Machihara-Nakanishi-Tsugawa, we prove local existence in the scale invariant class L2 by using null coordinates. Moreover, again using n
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Vogel, Thomas. "SOLITON SOLUTIONS OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS USING VARIATIONAL APPROXIMATIONS AND INVERSE SCATTERING TECHNIQUES." Doctoral diss., University of Central Florida, 2007. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/3506.

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Throughout the last several decades many techniques have been developed in establishing solutions to nonlinear partial differential equations (NPDE). These techniques are characterized by their limited reach in solving large classes of NPDE. This body of work will study the analysis of NPDE using two of the most ubiquitous techniques developed in the last century. In this body of work, the analysis and techniques herein are applied to unsolved physical problems in both the fields of variational approximations and inverse scattering transform. Additionally, a new technique for estimating the er
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Hoang, Luan Thach. "Asymptotic expansions of the regular solutions to the 3D Navier-Stokes equations and applications to the analysis of the helicity." Diss., Texas A&M University, 2005. http://hdl.handle.net/1969.1/2355.

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A new construction of regular solutions to the three dimensional Navier{Stokes equa- tions is introduced and applied to the study of their asymptotic expansions. This construction and other Phragmen-Linderl??of type estimates are used to establish su??- cient conditions for the convergence of those expansions. The construction also de??nes a system of inhomogeneous di??erential equations, called the extended Navier{Stokes equations, which turns out to have global solutions in suitably constructed normed spaces. Moreover, in these spaces, the normal form of the Navier{Stokes equations associate
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Cabarrubias, Bituin C. "Existence, uniqueness and homogenization results for a class of nonlinear PDE in perforated domains." Rouen, 2012. http://www.theses.fr/2012ROUES046.

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This thesis is devoted to the existence, uniqueness and homogenization results for a quasilinear elliptic problem with oscillating coefficients and with nonlinear Robin boundary condition in a periodically perforated domain. A suitable frowth conditions are assumed on the nonlinear boundary term and on the quasilinear term, some assumptions on the modulus of continuity introduced in Chipot [17] and weaker than a Lipschitz condition, are prescribed. For the existence and uniqueness of a solution, we consider a more general framework which, in particular, will imply the existence and uniqueness
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Guo, Sheng. "On Neumann Problems for Fully Nonlinear Elliptic and Parabolic Equations on Manifolds." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1571696906482925.

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Books on the topic "Nonlinear PDE"

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Taylor, Michael E. Pseudodifferential Operators and Nonlinear PDE. Birkhäuser Boston, 1991. http://dx.doi.org/10.1007/978-1-4612-0431-2.

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Kyûya, Masuda, and Suzuki Takashi, eds. Recent topics in nonlinear pde. Kinokuniya, 1987.

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Karch, Grzegorz. Self-similar solutions of nonlinear PDE. Insitute of Mathematics, Polish Academy of Sciences, 2006.

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Kyuya, Masuda, and Suzuki Takashi 1922-, eds. Recent topics in nonlinear PDE III. Kinokuniya Co., 1987.

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Mimura, Masayasu, and Takaaki Nishida. Recent topics in nonlinear PDE IV. North-Holland, 1989.

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1958-, Biler Piotr, and Karch Grzegorz, eds. Self-similar solutions of nonlinear PDE. Insitute of Mathematics, Polish Academy of Sciences, 2006.

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Christofides, Panagiotis D. Nonlinear and Robust Control of PDE Systems. Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-0185-4.

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Bethuel, Fabrice, Duvan Henao, and Angkana Rüland. Variational and PDE Methods in Nonlinear Science. Edited by Fabrice Bethuel, Giandomenico Orlandi, and Bianca Stroffolini. Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-031-87202-0.

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Krstic, Miroslav. Delay Compensation for Nonlinear, Adaptive, and PDE Systems. Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/978-0-8176-4877-0.

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Lang, Jens. Adaptive Multilevel Solution of Nonlinear Parabolic PDE Systems. Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-662-04484-1.

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Book chapters on the topic "Nonlinear PDE"

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Enns, Richard H., and George C. McGuire. "Nonlinear PDE Phenomena." In Nonlinear Physics with Mathematica for Scientists and Engineers. Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-1-4612-0211-0_10.

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Enns, Richard H., and George McGuire. "Nonlinear PDE Phenomena." In Nonlinear Physics with Maple for Scientists and Engineers. Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4684-0032-8_9.

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Enns, Richard H., and George C. McGuire. "Nonlinear PDE Phenomena." In Nonlinear Physics with Maple for Scientists and Engineers. Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1322-2_10.

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Krstic, Miroslav. "Other PDE-PDE Cascades." In Delay Compensation for Nonlinear, Adaptive, and PDE Systems. Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/978-0-8176-4877-0_20.

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Zhunussova, Zhanat. "Nonlinear PDE as Immersions." In Trends in Mathematics. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-12577-0_34.

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Evans, Lawrence. "Nonlinear first-order PDE." In Graduate Studies in Mathematics. American Mathematical Society, 2010. http://dx.doi.org/10.1090/gsm/019/03.

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Deuflhard, Peter. "PDE Boundary Value Problems." In Newton Methods for Nonlinear Problems. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-23899-4_8.

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Enns, Richard H., and George C. McGuire. "Nonlinear PDE Models: Soliton Solutions." In Computer Algebra Recipes. Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4613-0171-4_14.

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Popivanov, P. R. "Nonlinear PDE. Singularities, Propagation, Applications." In Nonlinear Hyperbolic Equations, Spectral Theory, and Wavelet Transformations. Birkhäuser Basel, 2003. http://dx.doi.org/10.1007/978-3-0348-8073-2_1.

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Taylor, Michael E. "Pseudodifferential operators and linear PDE." In Pseudodifferential Operators and Nonlinear PDE. Birkhäuser Boston, 1991. http://dx.doi.org/10.1007/978-1-4612-0431-2_2.

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Conference papers on the topic "Nonlinear PDE"

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Cohen, Benjamin G., Burcu Beykal, and George M. Bollas. "Selection of Fitness Criteria for Learning Interpretable PDE Solutions via Symbolic Regression." In The 35th European Symposium on Computer Aided Process Engineering. PSE Press, 2025. https://doi.org/10.69997/sct.199083.

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Physics-Informed Symbolic Regression (PISR) offers a pathway to discover human-interpretable solutions to partial differential equations (PDEs). This work investigates three fitness metrics within a PISR framework: PDE fitness, Bayesian Information Criterion (BIC), and a fitness metric proportional to the probability of a model given the data. Through experiments with Laplace�s equation, Burgers� equation, and a nonlinear wave equation, we demonstrate that incorporating information theoretic criteria like BIC can yield higher fidelity models while maintaining interpretability. Our results show
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Sun, Xiaoyu, Chuan Zhang, and He Yang. "Disturbance Observer-Based Hysteretic Quantized Fuzzy Control for Nonlinear Parabolic PDE System." In 2024 China Automation Congress (CAC). IEEE, 2024. https://doi.org/10.1109/cac63892.2024.10865241.

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Wang, Hao-Kun, Zi-Peng Wang, and Xuehua Yan. "Sampled-Data Fuzzy Control for Nonlinear Markov Jumping Parabolic PDE Systems with Deception Attacks." In 2024 43rd Chinese Control Conference (CCC). IEEE, 2024. http://dx.doi.org/10.23919/ccc63176.2024.10662806.

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Wei Wu and Ching-Tien Liou. "Output regulation of nonlinear PDE systems." In Proceedings of 2000 American Control Conference (ACC 2000). IEEE, 2000. http://dx.doi.org/10.1109/acc.2000.876926.

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El-Farra, N. H., A. Armaou, and P. D. Christofides. "Constrained nonlinear control of parabolic PDE systems." In Proceedings of 2000 American Control Conference (ACC 2000). IEEE, 2000. http://dx.doi.org/10.1109/acc.2000.878585.

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Wu, Huai-Ning, Hong-Du Wang, Yuyi Jin, and Ling Zhang. "Nonlinear disturbance observer based control for nonlinear dissipative PDE systems." In 2017 Chinese Automation Congress (CAC). IEEE, 2017. http://dx.doi.org/10.1109/cac.2017.8242997.

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Rahman, Lutfur, and Herbert G. Winful. "Dynamics of a Twin Stripe Semiconductor Laser Array: Coupled Mode Theory vs The PDE Model." In Nonlinear Dynamics in Optical Systems. Optica Publishing Group, 1992. http://dx.doi.org/10.1364/nldos.1992.thb3.

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In this paper we present numerical solutions for a partial differential equation (PDE) model1 for the dynamics of a twin stripe semiconductor laser array. The model includes carrier diffusion and the effects of propagation. A coupled-mode ordinary differential equation (ODE) model2 is then derived from this PDE model. The two models are compared in predicting the dynamical behavior of the laser array. We obtain good qualitative and quantitative agreement between the two models. The results obtained can be readily extended to larger arrays.
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Bekiaris-Liberis, Nikolaos, and Alexandre M. Bayen. "Nonlinear stabilization of a viscous Hamilton-Jacobi PDE." In 2014 IEEE 53rd Annual Conference on Decision and Control (CDC). IEEE, 2014. http://dx.doi.org/10.1109/cdc.2014.7039828.

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Hashemi, Seyed Mahdi, and Herbert Werner. "Observer-based LPV control of a nonlinear PDE." In 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC 2011). IEEE, 2011. http://dx.doi.org/10.1109/cdc.2011.6161232.

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Sun, Ji, and Jianxin Huang. "Optimal control of nonlinear time delay parabolic PDE." In 2017 International Conference on Intelligent Computing and Control Systems (ICICCS). IEEE, 2017. http://dx.doi.org/10.1109/iccons.2017.8250663.

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Reports on the topic "Nonlinear PDE"

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Yau, Stephen S. PDE, Differential Geometric and Algebraic Methods in Nonlinear Filtering. Defense Technical Information Center, 1993. http://dx.doi.org/10.21236/ada260967.

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Yau, Stephen S. PDE, Differential Geometric and Algebraic Methods for Nonlinear Filtering. Defense Technical Information Center, 1996. http://dx.doi.org/10.21236/ada310330.

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McWilliams, J. Algebraic coarsening methods for linear and nonlinear PDE and systems. Office of Scientific and Technical Information (OSTI), 2000. http://dx.doi.org/10.2172/15013125.

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Witelski, Thomas P., David G. Schaeffer, and Michael Shearer. A Discrete Model for an Ill-Posed Nonlinear Parabolic PDE. Defense Technical Information Center, 2001. http://dx.doi.org/10.21236/ada454438.

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Xin, Jack, and Yingyong Qi. A Perception and Nonlinear PDE Based Approach to Processing Spoken Words. Defense Technical Information Center, 2000. http://dx.doi.org/10.21236/ada391267.

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Yau, Stephen S. T. PDE, Differential Geometric, Algebraic, Wavelet and Parallel Computation Methods in Nonlinear Filtering. Defense Technical Information Center, 2003. http://dx.doi.org/10.21236/ada415460.

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Dupuis, Paul, and Jim X. Zhang. Explicit Solutions for a Class of Nonlinear PDE that Arise in Allocation Problems. Defense Technical Information Center, 2006. http://dx.doi.org/10.21236/ada458951.

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Chudnovsky, D. V., and G. V. Chudnovsky. Nonlinear Partial Differential Equations and Related Problems of Pade Approximations. Defense Technical Information Center, 1985. http://dx.doi.org/10.21236/ada172253.

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Verbrugge, Randal J., and Saeed Zaman. Post-COVID Inflation Dynamics: Higher for Longer. Federal Reserve Bank of Cleveland, 2023. http://dx.doi.org/10.26509/frbc-wp-202306.

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In the December 2022 Summary of Economic Projections (SEP), the median projection for four-quarter core PCE inflation in the fourth quarter of 2025 is 2.1 percent. This same SEP has unemployment rising by nine-tenths, to 4.6 percent, by the end of 2023. We assess the plausibility of this projection using a specific nonlinear model that embeds an empirically successful nonlinear Phillips curve specification into a structural model, identifying it via an underutilized data-dependent method. We model core PCE inflation using three components that align with those noted by Chair Powell in his Dece
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Dimakov, Serguei A., and V. K. Emel'yanov. Study Of Pre-Shaped Membrane Mirrors And Electrostatic Mirrors With Nonlinear-Optical Correction. Defense Technical Information Center, 2002. http://dx.doi.org/10.21236/ada410726.

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