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### Blow-up and continuation of solutions for some semilinear parabolic

#### Abstract

The following semilinear parabolic equations with nonlinear boundary conditions is studied.

$u_t=\Delta u-qu^{2q-1}$ in $B_1\times(0,T)$,

$\partial_{\nu}u=|u|^{q-1}u$ on $\partial B_1\times(0,T)$,

where $B_1\subset\R^n$ is the unit ball and $q>1$.

The finite time blow-up as well as a continuation of blow-up solutions

beyond the blow-up time is discussed for the multidimensional case.

It is revealed that the behavior of solutions for the multidimensional case

differs from that of the one dimensional case.

$u_t=\Delta u-qu^{2q-1}$ in $B_1\times(0,T)$,

$\partial_{\nu}u=|u|^{q-1}u$ on $\partial B_1\times(0,T)$,

where $B_1\subset\R^n$ is the unit ball and $q>1$.

The finite time blow-up as well as a continuation of blow-up solutions

beyond the blow-up time is discussed for the multidimensional case.

It is revealed that the behavior of solutions for the multidimensional case

differs from that of the one dimensional case.

#### Keywords

Blow-up; Continuation; Nonlinear boundary conditions

#### Full Text:

PDFDOI: http://dx.doi.org/10.14510%2Flm-ns.v32i2.37