具有记忆的对称双曲系统的耗散结构和渐近轮廓

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Journal of Hyperbolic Differential Equations Pub Date : 2021-06-01 DOI:10.1142/s0219891621500144

Shogo Taniue, S. Kawashima

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引用次数: 1

摘要

我们研究了具有记忆型耗散的对称双曲系统，并研究了它们在Craftsmaship条件下的耗散结构。我们处理了两种情况：记忆型扩散和记忆型弛豫，并观察到这两种情况的耗散结构有本质上的不同。即，我们证明了具有记忆型扩散的系统的耗散结构是标准型的，而具有记忆型弛豫的系统的损耗结构是规则损失型的。此外，我们还研究了[公式：见正文]解的渐近轮廓。在扩散情况下，证明了有记忆和无记忆的系统对于[公式：见正文]具有相同的渐近轮廓，这是由线性扩散波的叠加给出的。在对初始数据进行足够正则性假设的松弛情况下，我们也得到了相同的结果。

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Dissipative structure and asymptotic profiles for symmetric hyperbolic systems with memory

We study symmetric hyperbolic systems with memory-type dissipation and investigate their dissipative structures under Craftsmanship condition. We treat two cases: memory-type diffusion and memory-type relaxation, and observe that the dissipative structures of these two cases are essentially different. Namely, we show that the dissipative structure of the system with memory-type diffusion is of the standard type, while that of the system with memory-type relaxation is of the regularity-loss type. Moreover, we investigate the asymptotic profiles of the solutions for [Formula: see text]. In the diffusion case, it is proved that the systems with memory and without memory have the same asymptotic profile for [Formula: see text], which is given by the superposition of linear diffusion waves. We have the same result also in the relaxation case under enough regularity assumption on the initial data.

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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.