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Large time behavior of solutions to a class of doubly nonlinear parabolic equations. (English) Zbl 0787.35047
We study the large time asymptotic behavior of solutions of the doubly degenerate parabolic equation $$u_ t=\text{div} (| u |^{m- 1}| \nabla u |^{p-2} \nabla u)$$ in a cylinder $$\Omega \times \mathbb{R}^ +$$, with initial condition $$u(x,0) =u_ 0(x)$$ in $$\Omega$$ and vanishing on the parabolic boundary $$\partial \Omega \times \mathbb{R}^ +$$. Here $$\Omega$$ is a bounded domain in $$\mathbb{R}^ N$$, the exponents $$m$$ and $$p$$ satisfy $$m+p \geq 3$$, $$p>1$$, and the initial datum $$u_ 0$$ is in $$L^ 1(\Omega)$$.

##### MSC:
 35K65 Degenerate parabolic equations 35B40 Asymptotic behavior of solutions to PDEs
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