On a Semilinear Strongly Degenerate Parabolic Equation in an Unbounded Domain

J. Math. Sci. Univ. Tokyo
Vol. 20 (2013), No. 1, Page 91–113.

Anh, Cung The ; Tuyet. Le Thi
On a Semilinear Strongly Degenerate Parabolic Equation in an Unbounded Domain
We study the existence and long-time behavior of solutions to a semilinear strongly degenerate parabolic equation on $\Bbb R^N$ under an arbitrary polynomial growth order of the nonlinearity. To overcome some significant difficulty caused by the lack of compactness of the embeddings, the existence of global attractors is proved by combining the tail estimates method and the asymptotic $\textit{a priori}$ estimate method.
Keywords: semilinear strongly degenerate parabolic equation; weak solution; global attractor; tail-estimates method; asymptotic $\textit{a priori}$ estimate method.