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Extinction properties of semilinear heat equations with strong absorption. (English) Zbl 0655.35050
Summary: Consider the initial-boundary value problem for $u\sb t=\Delta u-\lambda u\quad q$ with $\lambda >0$, $0<q<1$; the initial data are nonnegative and the boundary data vanish. It is well known that the solution becomes extinct in finite time T, i.e., u(x,t) becomes identically zero for $t\ge T$, where T is some positive number. In this paper we study the profile of $x\to u(x,t)$ as $t\to T$.

35K60Nonlinear initial value problems for linear parabolic equations
35B40Asymptotic behavior of solutions of PDE
35B05Oscillation, zeros of solutions, mean value theorems, etc. (PDE)
35K20Second order parabolic equations, initial boundary value problems
Full Text: DOI
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