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Blow-up and continuation of solutions for some semilinear parabolic

Junichi Harada, Mitsuharu Otani

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.

Keywords


Blow-up; Continuation; Nonlinear boundary conditions

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