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Relevant bibliographies by topics / Nonlocal problems, nonlinear problems, stationary problems, evolutionary problems / Journal articles

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Journal articles on the topic 'Nonlocal problems, nonlinear problems, stationary problems, evolutionary problems'

Author: Grafiati

Published: 10 March 2023

Last updated: 31 July 2025

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1

Koleva, Miglena. "FINITE ELEMENT SOLUTION OF BOUNDARY VALUE PROBLEMS WITH NONLOCAL JUMP CONDITIONS." Mathematical Modelling and Analysis 13, no. 3 (2008): 383–400. http://dx.doi.org/10.3846/1392-6292.2008.13.383-400.

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We consider stationary linear problems on non‐connected layers with distinct material properties. Well posedness and the maximum principle (MP) for the differential problems are proved. A version of the finite element method (FEM) is used for discretization of the continuous problems. Also, the MP and convergence for the discrete solutions are established. An efficient algorithm for solution of the FEM algebraic equations is proposed. Numerical experiments for linear and nonlinear problems are discussed.

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2

Rodríguez-Bernal, Aníbal, and Silvia Sastre-Gómez. "Nonlinear nonlocal reaction-diffusion problem with local reaction." Discrete & Continuous Dynamical Systems 42, no. 4 (2022): 1731. http://dx.doi.org/10.3934/dcds.2021170.

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<p style='text-indent:20px;'>In this paper we analyse the asymptotic behaviour of some nonlocal diffusion problems with local reaction term in general metric measure spaces. We find certain classes of nonlinear terms, including logistic type terms, for which solutions are globally defined with initial data in Lebesgue spaces. We prove solutions satisfy maximum and comparison principles and give sign conditions to ensure global asymptotic bounds for large times. We also prove that these problems possess extremal ordered equilibria and solutions, asymptotically, enter in between these equi

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3

Ebeling, Werner. "Nonlinear dynamics of mixed evolutionary strategies for solving optimization problems." Izvestiya VUZ. Applied Nonlinear Dynamics 3, no. 3 (1995): 22–27. https://doi.org/10.18500/0869-6632-1995-3-3-22-27.

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Several elementary strategies of evolution are investigated and described by simple mathematical models, leading to a highdimensional system of coupled differential equations. The stationary states of the system correspond to relative optima and the stable attractor corresponds to the finai solution of the optimization problem. Special attention is devoted here to mixed Boltzmann - Darwin strategies modelling basic elements of thermodynamic and biological evolution respectively. A continous model leading to one p.d.e., the corresponding eigenvalue problem and several applications are discussed

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4

Borachok, Ihor. "Evolutionary-numerical algorithm for unsteady inverse geometric problems in double-connected domains." Journal of Applied and Numerical Analysis 2 (December 16, 2024): 18–29. https://doi.org/10.30970/ana.2024.2.18.

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Numerical solution of the problem of reconstruction of the inner boundary of the double-connected domain from the given Cauchy data on the outer part of the domain, for the heat and wave equations is considered. The inverse problem is reformulated as a minimization of the nonlinear functional. A real-valued genetic algorithm is used for the minimization. A tness function of the individual is proposed, for the calculation of which it is necessary to solve the non-stationary Dirichlet problem. For this problem, rst a semi discretization by the time variable is performed using the Rothe's method,

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5

FENG, BAO-FENG, and TAKUJI KAWAHARA. "TEMPORAL EVOLUTIONS AND STATIONARY WAVES FOR PERTURBED KDV EQUATION WITH NONLOCAL TERM." International Journal of Bifurcation and Chaos 12, no. 11 (2002): 2393–407. http://dx.doi.org/10.1142/s0218127402005972.

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Initial value problems as well as stationary solitary and periodic waves are investigated for a perturbed KdV equation including the Hilbert transform; ut + uux + βuxxx + η(ℋux - uxx) = 0 (η > 0). Multi-hump stationary solitary and periodic wave solutions are numerically identified. Furthermore, the close relation between the structure of the stationary waves and the behavior of the temporal evolutions is discussed in comparison with other perturbed KdV equations with different instability and dissipation terms. The results support some general features common to this type of nonlinear evol

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6

LEVKIN, DMYTRO, ANDRII KRAVTSOV, OLEXIY ZAVGORODNIY, and YANA KOTKO. "SOLUTION OF NONLINEAR OPTIMIZATION PROBLEMS OF HEAT TRANSFER THEORY." Herald of Khmelnytskyi National University. Technical sciences 347, no. 1 (2025): 221–26. https://doi.org/10.31891/2307-5732-2025-347-29.

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The article proposes mathematical models and computational methods for the solution of nonlinear problems of finding local extrema of the objective function. These mathematical models and computational methods create a computational structure for improving the accuracy of applied optimization problems. Computational mathematical models of thermal action on a multilayer material and laser action on an embryo have been developed. It should be noted that the computational mathematical model describing the laser effect on the embryo is a nonlocal boundary value problem with a system of evolutionar

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7

Huillet, Thierry E. "On Discrete-Time Multiallelic Evolutionary Dynamics Driven by Selection." Journal of Probability and Statistics 2010 (2010): 1–27. http://dx.doi.org/10.1155/2010/580762.

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We revisit some problems arising in the context of multiallelic discrete-time evolutionary dynamics driven by fitness. We consider both the deterministic and the stochastic setups and for the latter both the Wright-Fisher and the Moran approaches. In the deterministic formulation, we construct a Markov process whose Master equation identifies with the nonlinear deterministic evolutionary equation. Then, we draw the attention on a class of fitness matrices that plays some role in the important matter of polymorphism: the class of strictly ultrametric fitness matrices. In the random cases, we fo

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8

Krymov, Nikita E. "Estimating the Discrete Approximation Error in Solving the Stationary Radiant-and-Conduction Heat Transfer Problem in a System of Absolutely Black Square Rods." Vestnik MEI, no. 5 (2021): 128–34. http://dx.doi.org/10.24160/1993-6982-2021-5-128-134.

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Studying heat transfer processes in periodic media containing vacuum interlayers or cavities, heat through which is transferred by radiation, is of significant interest for applications. Direct numerical solution of such problems involves considerable computational efforts and becomes almost impossible for systems containing a large number of heat conducting elements, especially for 2D and 3D structures. Therefore, it is of issue to develop effective approximate solution methods for such problems. This publication continues a series of studies on developing and substantiating special discrete

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9

Kashchenko, Sergey. "Van der Pol Equation with a Large Feedback Delay." Mathematics 11, no. 6 (2023): 1301. http://dx.doi.org/10.3390/math11061301.

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The well-known Van der Pol equation with delayed feedback is considered. It is assumed that the delay factor is large enough. In the study of the dynamics, the critical cases in the problem of the stability of the zero equilibrium state are identified. It is shown that they have infinite dimension. For such critical cases, special local analysis methods have been developed. The main result is the construction of nonlinear evolutionary boundary value problems, which play the role of normal forms. Such boundary value problems can be equations of the Ginzburg–Landau type, as well as equations wit

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10

BREIT, D., L. DIENING, and S. SCHWARZACHER. "SOLENOIDAL LIPSCHITZ TRUNCATION FOR PARABOLIC PDEs." Mathematical Models and Methods in Applied Sciences 23, no. 14 (2013): 2671–700. http://dx.doi.org/10.1142/s0218202513500437.

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We consider functions u ∈ L∞(L2)∩Lp(W1, p) with 1 < p < ∞ on a time–space domain. Solutions to nonlinear evolutionary PDEs typically belong to these spaces. Many applications require a Lipschitz approximation uλ of u which coincides with u on a large set. For problems arising in fluid mechanics one needs to work with solenoidal (divergence-free) functions. Thus, we construct a Lipschitz approximation, which is also solenoidal. As an application we revise the existence proof for non-stationary generalized Newtonian fluids of Diening, Ruzicka and Wolf, Existence of weak solutions for unste

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11

Kazakov, Alexander. "Solutions to Nonlinear Evolutionary Parabolic Equations of the Diffusion Wave Type." Symmetry 13, no. 5 (2021): 871. http://dx.doi.org/10.3390/sym13050871.

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The article deals with nonlinear second-order evolutionary partial differential equations (PDEs) of the parabolic type with a reasonably general form. We consider the case of PDE degeneration when the unknown function vanishes. Similar equations in various forms arise in continuum mechanics to describe some diffusion and filtration processes as well as to model heat propagation in the case when the properties of the process depend significantly on the unknown function (concentration, temperature, etc.). One of the exciting and meaningful classes of solutions to these equations is diffusion (he

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12

Gordin, V. A. "COMPACT FINITE-DIFFERENCE SCHEMES FOR WEAKLY NON-LINEAR PROBLEMS AND BOUNDARY CONDITIONS IMITATING CAUCHY PROBLEM." XXII workshop of the Council of nonlinear dynamics of the Russian Academy of Sciences 47, no. 1 (2019): 32–37. http://dx.doi.org/10.29006/1564-2291.jor-2019.47(1).9.

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Compact finite-difference schemes are well known and provide high accuracy order for differential equation with constant coefficients. Algorithms for constructing compact schemes of the 4-th order for boundary value problems with variable (smooth or jump) coefficient are developed. For the diffusion equations with a smooth variable coefficient and the Levin – Leontovich equation, compact finite-difference schemes are also constructed and their 4-th order is experimentally confirmed. The method of constructing compact schemes of the 4-th order can be generalized to partial differential equation

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13

Smirnov, Aleksandr O., and Eugeni A. Frolov. "On the Propagation Model of Two-Component Nonlinear Optical Waves." Axioms 12, no. 10 (2023): 983. http://dx.doi.org/10.3390/axioms12100983.

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Currently, two-component integrable nonlinear equations from the hierarchies of the vector nonlinear Schrodinger equation and the vector derivative nonlinear Schrödinger equation are being actively investigated. In this paper, we propose a new hierarchy of two-component integrable nonlinear equations, which have an important difference from the already known equations. To construct the hierarchical equations, we use the monodromy matrix method, as first proposed by B.A. Dubrovin. The method we use consists of solving the following sequence of problems. First, using the Lax operator, we find th

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14

Drin, Yaroslav, Iryna Drin, and Svetlana Drin. "THE NONLOCAL PROBLEM FOR FRACTAL DIFFUSION EQUATION." Journal of Automation and Information sciences 1 (January 1, 2022): 47–55. http://dx.doi.org/10.34229/1028-0979-2022-1-5.

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Over the past few decades, the theory of pseudodifferential operators (PDO) and equations with such operators (PDE) has been intensively developed. The authors of a new direction in the theory of PDE, which they called parabolic PDE with non-smooth homogeneous symbols (PPDE), are Yaroslav Drin and Samuil Eidelman. In the early 1970s, they constructed an example of the Cauchy problem for a modified heat equation containing, instead of the Laplace operator, PDO, which is its square root. Such a PDO has a homogeneous symbol |σ|, which is not smooth at the origin. The fundamental solution of the C

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15

Coti, Zelati Vittorio, and Margherita Nolasco. "Existence of ground states for nonlinear, pseudo-relativistic Schrödinger equations." March 2, 2011. https://doi.org/10.4171/rlm/587.

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We study existence and regularity of positive stationary solutions for a class of nonlinear pseudo-relativistic Schrödinger equations. Such equations are characterized by a nonlocal pseudo-differential operator closely related to the square-root of the Laplacian. We investigate such problems using critical point theory after transforming them to elliptic equations with nonlinear Neumann boundary conditions.

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16

Van Anh, Nguyen Thi, Akhtar A. Khan, Zhenhai Liu, and Stanislaw Migorski. "Inverse Problems for Evolutionary Hemi-Quasi -Variational Inequalities with Applications." Set-Valued and Variational Analysis 33, no. 3 (2025). https://doi.org/10.1007/s11228-025-00763-5.

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Abstract This paper develops a comprehensive framework for estimating discontinuous or rapidly varying coefficients in evolutionary hemi-quasi -variational inequalities involving multi-valued monotone, semi-monotone, and pseudo-monotone maps. To establish that the coefficient-to-solution map is well-defined, we present new solvability results and demonstrate the weak compactness of the solution set for the considered hemi-quasi -variational inequalities. We introduce a novel variational selection to circumvent the commonly adopted but highly restrictive assumption that the sum of a monotone ma

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17

Chen, Shou-Ting, and Wen-Xiu Ma. "Nonlocal reduced integrable mKdV-type equations from a vector integrable hierarchy." Modern Physics Letters B, April 19, 2023. http://dx.doi.org/10.1142/s0217984923500458.

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This paper aims to present two hierarchies of nonlocal reduced integrable mKdV-type equations from a vector integrable hierarchy associated with a matrix Lie algebra, not being [Formula: see text] type. The key point is to make similarity transformations for the spectral matrix, which keep the associated zero curvature equations invariant and then there follow reduced nonlocal integrable mKdV-type equations. The success lies in determining a Laurent series solution to the corresponding reduced stationary zero curvature equation, which generates temporal matrix spectral problems in the zero cur

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18

KEMALBAY, Gulder. "Sarima-arch versus genetic programming in stock price prediction." Sigma Journal of Engineering and Natural Sciences – Sigma Mühendislik ve Fen Bilimleri Dergisi, 2021, 110–22. http://dx.doi.org/10.14744/sigma.2021.00001.

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In financial time series, one of the most challenging problems is predicting stock prices since the data generally exhibit deviation from the assumptions of stationary and homoscedasticity. For homogenous non-stationary time series, the Autoregressive Integrated Moving Average (ARIMA) model is the most commonly used linear class including some transformation such as differencing and variance stabilizing process. However, stock market data is often nonlinear, which indicates that more advanced methods are necessary. Genetic Programming (GP) is one of the evolutionary computational methods that

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