Electron. J. Diff. Eqns., Vol. 2004(2004), No. 53, pp. 1-12.

Qualitative properties of solutions to semilinear heat equations with singular initial data

Junjie Li

Abstract:
This article concerns the nonnegative solutions to the Cauchy problem
$$\displaylines{ u_t - \Delta u + b(x,t)|u|^{p-1}u = 0 \quad \hbox{in } \mathbb{R}^N \times (0,{\infty}), \cr u(x,0) = u_0(x) \quad \hbox{in } \mathbb{R}^N \,. }$$
We investigate how the comparison principle, extinction in finite time, instantaneous shrinking of support, and existence of solutions depend on the behaviour of the coefficient $b(x,t)$.

Submitted December 5, 2002. Published April 8, 2004.
Math Subject Classifications: 35B05, 35K55.
Key Words: Comparison principle, extinction, shrinking of support, existence.

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Junjie Li
Department of Mathematicas, Yuquan Campus
Zhejiang University, Hangzhou 310027, China
email: ljj@math.zju.edu.cn

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