## Behavior of solutions of certain quasilinear parabolic equations with power-type nonlinearities.(English. Russian original)Zbl 0957.35073

Sb. Math. 191, No. 3, 341-358 (2000); translation from Mat. Sb. 191, No. 3, 25-42 (2000).
The author studies non-negative solutions of the Cauchy problem for the equation $$u_t=\Delta u^m-u^p$$, $$(x,t)\in \mathbb{R}^N\times \mathbb{R}_+$$ with initial condition $$u(x,0)=u_0(x)$$, $$x\in \mathbb{R}^N$$, where $$0<p<1$$, $$p<m$$, $$u_0(x)$$ is a non-negative continuous function. For generalized solutions of this problems with initial data increasing at infinity, several results on their behaviour as $$t\rightarrow\infty$$ are established.

### MSC:

 35K65 Degenerate parabolic equations 35B40 Asymptotic behavior of solutions to PDEs 35K15 Initial value problems for second-order parabolic equations

### Keywords:

generalized solution; Cauchy problem
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