Inertial manifolds for a singularly non-autonomous semi-linear parabolic equations
| Autor: | Xinhua Li, Chunyou Sun |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Proceedings of the American Mathematical Society. 149:5275-5289 |
| ISSN: | 1088-6826 0002-9939 |
| DOI: | 10.1090/proc/15606 |
| Popis: | This paper devotes to the existence of an N N -dimensional inertial manifold for a class of singularly, i.e. A ( t ) A(t) may degenerate to 0 0 at some time t t , non-autonomous parabolic equations ∂ t u + A ( t ) u = F ( t , u ) + g ( x , t ) , t > τ ; u | t = τ = u τ ( x ) , x ∈ Ω , \begin{equation*} \partial _{t}u+A(t)u=F(t,u)+g(x,t),\;t>\tau ;\; \; u|_{t=\tau }=u_{\tau }(x),\;x\in \Omega , \end{equation*} where A ( t ) ≥ 0 A(t)\geq 0 for any t ≥ τ t\geq \tau , and Ω ⊂ R d \Omega \subset \mathbb {R}^{d} is a bounded domain with smooth boundary. Since the operator A ( t ) A(t) may degenerate, a compatibility condition for the operator A ( t ) A(t) and the nonlinear term F ( t , u ) F(t,u) was proposed to construct the inertial manifolds. |
| Databáze: | OpenAIRE |
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