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Nonexistence of positive solutions to a quasi-linear elliptic equation and blow-up estimates for a nonlinear heat equation. (English) Zbl 1141.35037

Summary: We prove blow-up estimates for a class of quasilinear heat equations (non-Newtonian filtration equations). These estimates extend results for semilinear heat equations (Newtonian filtration equations). Our method of proof is to first establish a nonexistence result for quasilinear elliptic equations and then established to blow-up estimates for a class of quasilinear heat equations.

MSC:

35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
76A05 Non-Newtonian fluids
76S05 Flows in porous media; filtration; seepage
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References:

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