Regularity of invariant sets in semilinear damped wave equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:247

Article

Prizzi, Martino

关键词: Damped wave equation;    Invariant set;    Regularity;   

DOI  :  10.1016/j.jde.2009.08.011

来源: Elsevier

【 摘 要 】

Under fairly general assumptions, we prove that every compact invariant Subset I of the semiflow generated by the semilinear damped wave equation epsilon u(tt) + u(t) + beta(x)u - Sigma(ij)(a(ij)(x)u(xj))(xi) = f(x, u), (t, x) is an element of [0, +infinity[ x Omega, u = 0, (t, x) is an element of [0, +infinity[ x partial derivative Omega, in H-0(1)(Omega) x L-2(Omega) is in fact bounded in D(A) x H-0(1)(Omega). Here Omega is an arbitrary, possibly unbounded, domain in R-3, Au = beta(x)u - Sigma(ij)(a(ij)(x)u(xj))(xi) is a positive selfadjoint elliptic operator and f(x, u) is a nonlinearity of critical growth. The nonlinearity f(x, u) needs not to satisfy any dissipativeness assumption and the invariant subset I needs not to be an attractor. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free