Mixed boundary valued problems for linear and nonlinear wave equations in domains with fractal boundaries

被引：5
|
作者：
Dekkers, Adrien [1 ]
Rozanova-Pierrat, Anna [1 ]
Teplyaev, Alexander [2 ]
机构：
[1] Univ Paris Saclay, Lab Math & Informat Complex & Syst, Cent Supelec, 3 Rue Joliot Curie, F-91190 Gif Sur Yvette, France
[2] Univ Connecticut, Dept Math, Storrs, CT 06269 USA
来源：
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2022年 / 61卷 / 02期
关键词：
BESOV-SPACES; MAXIMAL REGULARITY; SOBOLEV EXTENSION; WELL-POSEDNESS; BANACH-SPACES; HEAT-EQUATION; CONTROLLABILITY; APPROXIMATIONS; EXTENDABILITY; WESTERVELT;
D O I：
10.1007/s00526-021-02159-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The weak well-posedness, with the mixed boundary conditions, of the strongly damped linear wave equation and of the non linear Westervelt equation is proved in a large natural class of Sobolev admissible non-smooth domains. In the framework of uniform domains in R-2 or R-3 we also validate the approximation of the solution of the Westervelt equation on a fractal domain by the solutions on the prefractals using the Mosco convergence of the corresponding variational forms.
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页数：44
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