To properties of solutions to reaction-diffusion equation with double nonlinearity with distributed parameters. (English) Zbl 1522.35311
Summary: The properties of solutions of self-similar and approximately self-similar system of the reaction-diffusion with double nonlinearity are investigated. The influence of numerical parameters to an evolution of the studied process is established. The existence of finite and quenching solutions is proved and their asymptotic behavior at the infinity is described. The condition of global solvability to the Cauchy problem, generalizing the results of other authors, is found. Knerr-Kersner type estimate for free boundary is obtained. The results of numerical experiments are enclosed.
MSC:
| 35K57 | Reaction-diffusion equations |
| 35K65 | Degenerate parabolic equations |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35K60 | Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations |
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