Normal trace inequalities and decay of solutions to the nonlinear Maxwell system with absorbing boundary

被引：0

作者：

Nutt, Richard ^{[1
]}

Schnaubelt, Roland ^{[1
]}

机构：

[1] Karlsruhe Inst Technol, Dept Math, Englerstr 2, D-76131 Karlsruhe, Germany

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2024年 / 532卷 / 01期

关键词：

Quasilinear Maxwell system; Absorbing boundary conditions; Nonhomogenous anisotropic; materials; Trace regularity; Exponential decay; EQUATIONS; STABILIZATION; STABILITY; FEEDBACK;

D O I：

10.1016/j.jmaa.2023.127915

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the quasilinear Maxwell system with a strictly positive, state dependent boundary conductivity. For small data we show that the solution exists for all times and decays exponentially to 0. As in related literature we assume a nontrapping condition. Our approach relies on a new trace estimate for the corresponding non-autonomous linear problem, an observability-type estimate, and a detailed regularity analysis. The results are improved in the linear autonomous case, using properties of the Helmholtz decomposition in Sobolev spaces of (small) negative order.(c) 2023 Elsevier Inc. All rights reserved.

引用

页数：35

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