Quenching Rate for the Porous Medium Equation with a Singular Boundary Condition

Quenching Rate for the Porous Medium Equation with a Singular Boundary Condition

We study the porous medium equation   = , 0 < < , > m t x t  0 t xx . We prove finite time quenching for the solution at the boundary . We also estabu u with a singular boundary condition       0, = 0, m x u t u   = 0 x lish the quenching rate and asymptotic behavior on the quenching point.

Porous medium equation with absorption and a nonlinear boundary condition

In this paper we study a porous medium equation with a nonlinear absorption term and a nonlinear boundary condition. We prove existence of weak solutions and also we establish some uniqueness and non uniqueness results for certain range of the parameters that appear in the problem. Finally we deal with the existence of global solutions in time or blow-up. We find in which region of parameters t...

Quenching for a Non-Newtonian Filtration Equation with a Singular Boundary Condition

and Applied Analysis 3 Next, we deal with the quenching rate. Before we establish upper bounds for the quenching rate, we introduce the following hypothesis: H1 ψ ′′ u g u ≥ 2 p − 1 ψ ′ u g ′ u , ψ ′ u p − 2 g ′2 u g u g ′′ u ≥ ψ ′′ u g u g ′ u . Theorem 1.2. Suppose that the conditions of Theorem 1.1 and the hypothesis H1 hold. Then there exists a positive constant C1 such that ∫u 1,t 0 ψ ′ s ...

The quenching behavior of a nonlinear parabolic equation with a singular boundary condition

In this paper, we study the quenching behavior of solution of a nonlinear parabolic equation with a singular boundary condition. We prove finite-time quenching for the solution. Further, we show that quenching occurs on the boundary under certain conditions. Furthermore, we show that the time derivative blows up at quenching point. Also, we get a lower solution and an upper bound for quenching ...

Homogenization of the Stokes equation with mixed boundary condition in a porous medium