On the well-posedness and numerical approximation of a nonlocal thermistor problem

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2026-07-01 Epub Date: 2026-01-29 DOI:10.1016/j.cnsns.2026.109810

Ibrahim Dahi , Moulay Rchid Sidi Ammi , Mostafa Tahiri , Delfim F.M. Torres

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Abstract

In this paper, we examine a broader variant of the nonlocal thermistor problem, which the heat diffusion that occurs when an electric current flows through a substance. which characterizes the heat diffusion phenomenon that occurs when an electric current flows through a substance. We analyze the doubly nonlinear problem in which the equation describing the temperature evolution has a nonlocal term on the right-hand side whereasthe first nonlinearity is present in the diffusion term. By virtue of an approximation technique, we establish the existence and uniqueness of a global weak solution to the considered problem in Sobolev spaces.Using the finite-difference approach, this paper offers a useful summary of numerical solutions in two dimensions to the non-local thermistor problem. The analysis includes a rigorous error estimation and is supported by numerical experiments that confirm the effectiveness and robustness of the proposed scheme, demonstrating second-order convergence in space as well as first-order convergence in time.

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非局部热敏电阻问题的适定性和数值逼近

在本文中，我们研究了非局部热敏电阻问题的一个更广泛的变体，它是当电流流过物质时发生的热扩散。它描述了当电流流过物质时发生的热扩散现象。我们分析了双非线性问题，其中描述温度演化的方程的右边有一个非局部项，而第一个非线性存在于扩散项。利用逼近技术，我们建立了Sobolev空间中所考虑问题的整体弱解的存在唯一性。本文利用有限差分方法，总结了非局部热敏电阻问题的二维数值解。该分析包括严格的误差估计，并通过数值实验验证了所提出方案的有效性和鲁棒性，证明了该方案在空间上的二阶收敛和在时间上的一阶收敛。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.