## Blow-up analysis for a nonlinear diffusion equation with nonlinear boundary conditions.(English)Zbl 1056.35087

Summary: The blow-up rate for a nonlinear diffusion equation $$u_t= (u^m)_{xx}+ u^p$$, $$0< x< 1$$ with a nonlinear boundary condition $$(u^m)_x= u^q$$ at $$x=0$$, $$(u^m)_x= 0$$ at $$x=1$$ is established together with the necessary and sufficient blow-up conditions.

### MSC:

 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations 35K57 Reaction-diffusion equations 35B40 Asymptotic behavior of solutions to PDEs 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 35K65 Degenerate parabolic equations
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### References:

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