Non-delay limit in the energy space from the nonlinear damped wave equation to the nonlinear heat equation

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Journal of Hyperbolic Differential Equations Pub Date : 2021-06-06 DOI:10.1142/s0219891622500126

Takahisa Inui, Shuji Machihara

引用次数: 2

Abstract

We consider a singular limit problem from the damped wave equation with a power type nonlinearity (NLDW) to the corresponding heat equation (NLH). We call our singular limit problem non-delay limit. We show that the solution of NLDW goes to the one of NLH in [Formula: see text] topology under the both [Formula: see text] regularity solutions. We also obtain the positive convergence rate in the weaker topology [Formula: see text]. Moreover, with restriction of the range of power, if the solution to NLH is global and decays to zero, then we get the global-in-time uniform convergence of the non-delay limit.

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从非线性阻尼波动方程到非线性热方程在能量空间上的非延迟极限

研究了一类由幂型非线性阻尼波动方程(NLDW)到相应热方程的奇异极限问题。我们称奇异极限问题为非延迟极限。我们证明了在两种[公式:见文]正则解下，NLDW的解都趋向于[公式:见文]拓扑中NLH的解。我们也得到了弱拓扑下的正收敛率[公式:见文]。此外，在功率范围的限制下，如果NLH的解是全局的并且衰减到零，则得到了非延迟极限的全局实时一致收敛性。

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

Journal of Hyperbolic Differential Equations 数学-物理：数学物理

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： This journal publishes original research papers on nonlinear hyperbolic problems and related topics, of mathematical and/or physical interest. Specifically, it invites papers on the theory and numerical analysis of hyperbolic conservation laws and of hyperbolic partial differential equations arising in mathematical physics. The Journal welcomes contributions in: Theory of nonlinear hyperbolic systems of conservation laws, addressing the issues of well-posedness and qualitative behavior of solutions, in one or several space dimensions. Hyperbolic differential equations of mathematical physics, such as the Einstein equations of general relativity, Dirac equations, Maxwell equations, relativistic fluid models, etc. Lorentzian geometry, particularly global geometric and causal theoretic aspects of spacetimes satisfying the Einstein equations. Nonlinear hyperbolic systems arising in continuum physics such as: hyperbolic models of fluid dynamics, mixed models of transonic flows, etc. General problems that are dominated (but not exclusively driven) by finite speed phenomena, such as dissipative and dispersive perturbations of hyperbolic systems, and models from statistical mechanics and other probabilistic models relevant to the derivation of fluid dynamical equations. Convergence analysis of numerical methods for hyperbolic equations: finite difference schemes, finite volumes schemes, etc.