A very singular solution of a quasilinear degenerate diffusion equation with absorption

Peletier, L. A.; Wang, Jun Yu

doi:10.1090/S0002-9947-1988-0940229-6

A very singular solution of a quasilinear degenerate diffusion equation with absorption
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by L. A. Peletier and Jun Yu Wang

Trans. Amer. Math. Soc. 307 (1988), 813-826

DOI: https://doi.org/10.1090/S0002-9947-1988-0940229-6

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Abstract:

The object of this paper is to study the existence of a nonnegative solution of the Cauchy problem \[ {u_t} = \operatorname {div} (|\nabla u{|^{p - 2}}\nabla u) - {u^q},\qquad u(x, 0) = 0\quad {\text {if}}\;x \ne 0,\] which is more singular at $(0, 0)$ than the fundamental solution of the corresponding equation without the absorption term.

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