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Blow-up in nonlinear heat equations. (English) Zbl 1180.35130

The authors study the blow-up of solutions of nonlinear heat equations. And it shows that for an open set of even initial data which are characterized roughly by having maxima at the origin, the solutions blow up in finite time and at a single point. We find the universal blow-up profile and remainder estimates.
Reviewer: Jiaqi Mo (Wuhu)

MSC:

35B44 Blow-up in context of PDEs
35K57 Reaction-diffusion equations
35K55 Nonlinear parabolic equations
35K15 Initial value problems for second-order parabolic equations
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