On the asymptotic behavior of solutions to a class of degenerate parabolic problems of Neumann type
The author obtains decay estimates for the solution of \[ u_t=\Delta(\Phi\circ u)-g\circ u \quad\text{on } \Omega\times(0,\infty), \qquad u(\cdot,0)=\varphi \quad\text{on }\Omega, \] \[ \partial_\nu u(x,t)=0, \qquad (x,t)\in\partial\Omega \times (0,\infty) \] in case that \(\Omega\subset{\mathbb R}^N\) is a smooth, bounded domain, \(\Phi\in C({\mathbb R})\cap C^1({\mathbb R}\setminus\{0\})\), \(\Phi(0)=0\), \(\Phi'(z)>0\) for \(z\neq 0\), \(g\in C({\mathbb R})\) is strictly increasing, \(g(0)=0\) and \(\varphi\in L^1(\Omega)\). Earlier work by \textit{N. D. Alikakos} and \textit{R. Rostamian} [Indiana Univ. Math. J. 30, 749-785 (1981; Zbl 0598.76100); Nonlinear Anal., Theory Methods Appl. 6, 637-647 (1982; Zbl 0488.35045)] is generalized.
scientific article; zbMATH DE number 1529451