Abstract
This paper is concerned with the quenching phenomenon for the one-dimensional non-Newtonian filtration equation with both source term and Neumann boundary condition. With two different kinds of initial data, we prove that the solution must quench in a finite time and the time derivative blows up at a quenching point. The corresponding quenching rate and a lower bound for the quenching time are also obtained.
Highlights
In this paper, we study the following problem: ut = |ux|p– ux x + ( – u)–h, < x , ( . )ux(, t) =, ux(, t) = –u–q(, t), t >, u(x, ) = u (x), ≤ x ≤, t→T – In, Kawarada [ ] first studied the quenching phenomenon for the semilinear heat equation ut = uxx + ( – u)
Since quenching phenomena for semilinear parabolic equations have been studied by many researchers; see for ex
Quenching phenomenon is dependent on the singular term of the model
Summary
The quenching behavior describes the phenomenon that there exists a finite time T such that the solution u(x, t) of the problem The authors proved that the solution quenches only at x = a, the time derivative ut blows up. Few works were concerned with singular or degenerate parabolic equations [ – ], where only models with one nonlinear source are studied.
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