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Blow-up phenomena for some nonlinear parabolic problems. (English) Zbl 1159.35382

Summary: We consider the blow-up of solutions of equations of the form \[ u_t=\text{div}(\rho(|\nabla u|^2)\text{grad}\,u)+f(u) \] by means of a differential inequality technique. A lower bound for blow-up time is determined if blow-up does occur as well as a criterion for blow-up and conditions which ensure that blow-up cannot occur.

MSC:

35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35K55 Nonlinear parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
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