Wave equation with viscoelastic acoustic boundary conditions and supercritical source term

被引：8

作者：

Vicente, A. ^{[1
]}

机构：

[1] Univ Estadual Oeste Parana, Ctr Ciencias Exatas & Tecnol, Cascavel, PR, Brazil

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2023年 / 363卷

关键词：

Stability; Wave equation; Acoustic boundary conditions; Existence and uniqueness of solution; Non-locally; reacting boundary; Supercritical source; UNIFORM DECAY-RATES; HYPERBOLIC EQUATION; PARABOLIC PROBLEMS; CONTINUOUS DEPENDENCE; UNBOUNDED-DOMAINS; WELL-POSEDNESS; PAST HISTORY; STABILITY; STABILIZATION; ATTRACTORS;

D O I：

10.1016/j.jde.2023.03.029

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is concerning with the study of Hadamard well-posedness for a wave equation with nonlinear internal damping and acoustic boundary conditions for non-locally reacting boundary. On the boundary we consider the action of viscoelastic and frictional damping and also a supercritical source term. To prove the existence of solution we use semigroup theory. We also study the asymptotic behavior of the functional energy associated to the problem. (c) 2023 Elsevier Inc. All rights reserved.

引用

页码：422 / 464

页数：43

共 54 条

[1] Nonlinear wave equation with Dirichlet and Acoustic boundary conditions: theoretical analysis and numerical simulation [J].

Alcantara, Adriano A. ;

Carmo, Bruno A. ;

Clark, Haroldo R. ;

Guardia, Ronald R. ;

Rincon, Mauro A. .

COMPUTATIONAL & APPLIED MATHEMATICS, 2022, 41 (04)

[2] Theoretical analysis and numerical simulation for a hyperbolic equation with Dirichlet and acoustic boundary conditions [J].

Alcantara, Adriano A. ;

Clark, Haroldo R. ;

Rincon, Mauro A. .

COMPUTATIONAL & APPLIED MATHEMATICS, 2018, 37 (04) :4772-4792

[3] Long-time behavior of a quasilinear viscoelastic equation with past history [J].

Araujo, Rawlilson de Oliveira ;

Ma, To Fu ;

Qin, Yuming .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 254 (10) :4066-4087

[4] ACOUSTIC BOUNDARY-CONDITIONS [J].

BEALE, JT ;

ROSENCRA.SI .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 80 (06) :1276-1278

[5] On a wave equation with supercritical interior and boundary sources and damping terms [J].

Bociu, Lorena ;

Rammaha, Mohammad ;

Toundykov, Daniel .

MATHEMATISCHE NACHRICHTEN, 2011, 284 (16) :2032-2064

[6] Local Hadamard well-posedness for nonlinear wave equations with supercritical sources and damping [J].

Bociu, Lorena ;

Lasiecka, Irena .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 249 (03) :654-683

[7] Stability for semilinear hyperbolic coupled system with frictional and viscoelastic localized damping [J].

Cavalcanti, M. M. ;

Cavalcanti, V. N. Domingos ;

Martinez, V. H. Gonzalez ;

Peralta, V. A. ;

Vicente, A. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 269 (10) :8212-8268

[8] Exponential stability for the wave model with localized memory in a past history framework [J].

Cavalcanti, M. M. ;

Domingos Cavalcanti, V. N. ;

Jorge Silva, M. A. ;

de Souza Franco, A. Y. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2018, 264 (11) :6535-6584

[9] Attractors for wave equations with degenerate memory [J].

Cavalcanti, M. M. ;

Fatori, L. H. ;

Ma, T. F. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 260 (01) :56-83

[10] STABILITY FOR THE MIXED PROBLEM INVOLVING THE WAVE EQUATION, WITH LOCALIZED DAMPING, IN UNBOUNDED DOMAINS WITH FINITE MEASURE [J].

Cavalcanti, Marcelo M. ;

Dias Silva, Flavio R. ;

Domingos Cavalcanti, Valeria N. ;

Vicente, Andre .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2018, 56 (04) :2802-2834

← 1 2 3 4 5 6 →