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

共 50 条

[21] GLOBAL EXISTENCE AND ENERGY DECAY OF SOLUTIONS TO A NONLINEAR TIMOSHENKO BEAM SYSTEM WITH A DELAY TERM
Benaissa, Abbes
Bahlil, Mounir
TAIWANESE JOURNAL OF MATHEMATICS, 2014, 18 (05): : 1411 - 1437
[22] General decay for a nonlinear Bresse system with memory conditions on part of the boundary
Chen, Kewang
Liu, Wenjun
Yu, Jun
APPLICABLE ANALYSIS, 2021, 100 (09) : 1949 - 1971
[23] On multiplicity of semi-classical solutions to a nonlinear Maxwell-Dirac system
Ding, Yanheng
Ruf, Bernhard
JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 260 (07) : 5565 - 5588
[24] Global solutions and exponential decay for nonlinear coupled system of beam equations of Kirchhoff type with memory in a domain with moving boundary
Santos, M. L.
Soares, U. R.
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2007, (09) : 1 - 24
[25] General energy decay of solutions for a weakly dissipative Kirchhoff equation with nonlinear boundary damping
Peyravi, Amir
ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2017, 33 (02): : 401 - 408
[26] Global existence and asymptotic decay of solutions to the non-isentropic Euler-Maxwell system
Feng, Yue-Hong
Wang, Shu
Kawashima, Shuichi
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2014, 24 (14) : 2851 - 2884
[27] The minimal decay regularity of smooth solutions to the Euler-Maxwell two-fluid system
Xu, Jiang
Kawashima, Shuichi
JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2016, 13 (04) : 719 - 733
[28] WELL-POSEDENESS AND ENERGY DECAY OF SOLUTIONS TO A BRESSE SYSTEM WITH A BOUNDARY DISSIPATION OF FRACTIONAL DERIVATIVE TYPE
Benaissa, Abbes
Kasmi, Abderrahmane
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2018, 23 (10): : 4361 - 4395
[29] Ground-state solutions for the electrostatic nonlinear Klein-Gordon-Maxwell system
Wang, Feizhi
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (14) : 4796 - 4803
[30] Existence and concentration of semi-classical solutions for a nonlinear Maxwell-Dirac system
Ding, Yanheng
Wei, Juncheng
Xu, Tian
JOURNAL OF MATHEMATICAL PHYSICS, 2013, 54 (06)

← 1 2 3 4 5 →