LOCAL WELL POSEDNESS, ASYMPTOTIC BEHAVIOR AND ASYMPTOTIC BOOTSTRAPPING FOR A CLASS OF SEMILINEAR EVOLUTION EQUATIONS OF THE SECOND ORDER IN TIME
| Contribuinte(s) |
UNIVERSIDADE DE SÃO PAULO |
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| Data(s) |
18/04/2012
18/04/2012
2009
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| Resumo |
A class of semilinear evolution equations of the second order in time of the form u(tt)+Au+mu Au(t)+Au(tt) = f(u) is considered, where -A is the Dirichlet Laplacian, 92 is a smooth bounded domain in R(N) and f is an element of C(1) (R, R). A local well posedness result is proved in the Banach spaces W(0)(1,p)(Omega)xW(0)(1,P)(Omega) when f satisfies appropriate critical growth conditions. In the Hilbert setting, if f satisfies all additional dissipativeness condition, the nonlinear Semigroup of global solutions is shown to possess a gradient-like attractor. Existence and regularity of the global attractor are also investigated following the unified semigroup approach, bootstrapping and the interpolation-extrapolation techniques. CNPq[300.889/92-5] FAPESP, Brazil[03/10042-0] |
| Identificador |
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v.361, n.5, p.2567-2586, 2009 0002-9947 http://producao.usp.br/handle/BDPI/15926 http://www.ams.org/journals/tran/2009-361-05/S0002-9947-08-04789-2/S0002-9947-08-04789-2.pdf |
| Idioma(s) |
eng |
| Publicador |
AMER MATHEMATICAL SOC |
| Relação |
Transactions of the American Mathematical Society |
| Direitos |
openAccess Copyright AMER MATHEMATICAL SOC |
| Palavras-Chave | #Evolution equations of the second order in time #existence #uniqueness and continuous dependence of solutions on initial conditions #asymptotic behavior of solutions #attractors #regularity #critical exponents #DAMPED WAVE-EQUATIONS #GLOBAL ATTRACTORS #EXISTENCE #SYSTEMS #Mathematics |
| Tipo |
article original article publishedVersion |
