A structurally damped plate equation with Dirichlet-Neumann boundary conditions

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:259

Article

Denk, Robert¹  Schnaubelt, Roland² 

[1] Univ Konstanz, Fachbereich Math & Stat, D-78457 Constance, Germany

[2] Karlsruhe Inst Technol, Dept Math, D-76128 Karlsruhe, Germany

关键词: Structurally damped plate equation;    Clamped boundary condition;    R-sectoriality;    Optimal regularity;    Operator-valued Fourier multipliers;    Exponential stability;   

DOI  :  10.1016/j.jde.2015.02.043

来源: Elsevier

【 摘 要 】

We investigate sectoriality and maximal regularity in L-p-L-q-Sobolev spaces for the structurally damped plate equation with Dirichlet-Neumann (clamped) boundary conditions. We obtain unique solutions with optimal regularity for the inhomogeneous problem in the whole space, in the half-space, and in bounded domains of class C-4. It turns out that the first-order system related to the scalar equation on R-n is sectorial only after a shift in the operator. On the half-space one has to include zero boundary conditions in the underlying function space in order to obtain sectoriality of the shifted operator and maximal regularity for the case of homogeneous boundary conditions. We further show that the semigroup solving the problem on bounded domains is exponentially stable. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free