Quenching Phenomenon For Nonlinear Parabolic Problems With Absorption Sources

In the quenching phenomenon for nonlinear evolution equations, absorption sources play an important role. The nonlinear evolution equations with only one absorption source are the usual case to be considered. But there are no more detailed analysis on the equations with two or more than two absorption sources. Since the absorbtion sources can generate significant impacts on the quenching phenomenon, it is an interesting thing to study the behavior of the equations with two or more absorption sources. Therefore, this thesis mainly focuses on the impact of the complex structure of absorption sources on the quenching phenomenon and its properties.In Section 1, we first introduce the definition of quenching of the problem and its applica-tions background. Then we introduced the research history of quenching phenomenon for the nonlinear parabolic equations in recent years. Finally, we give the outline of this thesis.In Section 2, we investigate initial-boundary value problems for nonlinear parabolic equa-tions with two absorption sources. The definition of quenching is given, and the local existence of the solution for the problem is obtained. By maximum principle, we show that the solution (?) of the problem quenches in finite time. And under some conditions, we estimate the upper and lower bounds of its quenching time. Finally, we also carried out the numerical simulation.In Section 3, we investigate initial-boundary value problems for nonlinear parabolic equa-tions with combined power-type nonlinearities. The local existence of the solution for the prob-lem is obtained. It is proved that the solution u of the problem quenches in finite time. And under a series of conditions, the estimates of the upper and lower bounds for its quenching time is obtained. Finally, the numerical simulation are shown.In Section 4, we investigate initial-boundary value problems for nonlinear parabolic equa-tions with a positive and a negative absorption sources. we show that the solution a of the problem quenches in finite time and estimate the upper and lower bounds of its quenching time. Finally, we also carried out the numerical simulation.