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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
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