Existence of a global attractor for semilinear dissipative wave equations on RN

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:157

Article

Karachalios, NI ; Stavrakakis, NM

关键词: dynamical systems;    attractors;    hyperbolic equations;    nonlinear problems;    semigroups;    unbounded domains;    generalised Sobolev spaces;   

DOI  :  10.1006/jdeq.1999.3618

来源: Elsevier

【 摘 要 】

We consider the semilinear hyperbolic problem u(tt) + delta u(t) - phi(x) Delta u + lambda f(u) = eta(x), x epsilon R-N, t > 0, with the initial conditions u(x,0) = u(0)(x) and u(t)(x, 0) = u(1)(x) in the case where N greater than or equal to 3 and (phi(x))(-1) : = g(x) lies in L-N/2(R-N). The energy space chi(0) = G(1,2)(R-N) x L-g(2) (R-N) is introduced, to overcome the difficulties related with the noncompactness of operators which arise in unbounded domains. We derive various estimates to show local existence of solutions and existence of a global attractor in chi(0). The compactness of the embedding L-1,L-2(R-N) subset of L-g(2)(R-N) is widely applied. (C) 1999 Academic Press.

【 授权许可】

Free