| Summary: | 碩士 === 國立嘉義大學 === 應用數學系研究所 === 96 === In this thesis, we study a porous medium equation with a nonlinear boundary condition and an initial condition. Our main purpose is to study blow-up and quenching phenomenon. Using the comparison principle for the nonlinear Neumann boundary condition and the initial condition, we give the criteria for blow-up and quenching by initial datum. Furthermore, we also study the stationary problem, establish the existence, uniqueness and instability of the stationary solution.
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