Large time behavior of solutions to a class of doubly nonlinear parabolic equations. (English) Zbl 1199.35188

Summary: We study the large time asymptotic behavior of solutions of the doubly degenerate parabolic equation \(u_{t}=\operatorname {div}(u^{m-1}| Du| ^{p-2}Du)-u^{q}\) with an initial condition \(u(x,0)=u_{0}(x)\). Here the exponents  \(m\), \(p\) and \(q\) satisfy \(m+p\geq 3\), \(p>1\) and \(q>m+p-2\).


35K65 Degenerate parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
35K55 Nonlinear parabolic equations
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