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Blow-up phenomena for some nonlinear parabolic problems under mixed boundary conditions. (English) Zbl 1201.35057
Summary: We determine the lower bound for the blow-up time of solution to equations of the form $u_t = \text{div} (\rho (|\nabla u|^2)\operatorname{grad} u) + f(u)$ if the solution blows up. Conditions which ensure, that blow-up does not occur, are also presented.

MSC:
35B44Blow-up (PDE)
35K59Quasilinear parabolic equations
35K20Second order parabolic equations, initial boundary value problems
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References:
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