Asymptotic behavior of solutions for the porous media equations with nonlinear norm-type sources. (English) Zbl 1513.35290
Summary: In the paper, the asymptotic behavior of the solution for the parabolic equation system of porous media coupled by three variables and with weighted nonlocal boundaries and nonlinear internal sources is studied. by constructing the upper and lower solutions with the ordinary differential equation as well as introducing the comparison theorem, the global existence and finite time blow-up of the solution of parabolic equations of porous media coupled by the power function and the logarithm function are obtained. The differential inequality technique is used to obtain the lower bounds on the blow up time of the above equations under Dirichlet and Neumann boundary conditions.
MSC:
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 35K55 | Nonlinear parabolic equations |
| 35K60 | Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations |
| 35K65 | Degenerate parabolic equations |
Keywords:
porous media equations; norm-type sources; global existence; finite time blow-up; blow up timeReferences:
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