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Blow-up set for a semilinear heat equation with small diffusion. (English) Zbl 1204.35054
The blow-up set of positive solutions of a semilinear heat equation is studied. It is shown that, under suitable assumptions on the initial data, the solutions blow-up only near the maximum points of the initial data provided the diffusion coefficient is small enough.

MSC:
35B44 Blow-up in context of PDEs
35K57 Reaction-diffusion equations
35B40 Asymptotic behavior of solutions to PDEs
35K58 Semilinear parabolic equations
35K15 Initial value problems for second-order parabolic equations
35B09 Positive solutions to PDEs
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