Quenching Behavior for a Nonlinear Parabolic Equation with Nonlinear Boundary Flux
Zhe Jia
Institute of Mathematics, School of Mathematics Science, Nanjing Normal University, Jiangsu Nanjing 210023, China.
Zuodong Yang *
Institute of Mathematics, School of Mathematics Science, Nanjing Normal University, Jiangsu Nanjing 210023, China and School of Teacher Education, Nanjing Normal University, Jiangsu Nanjing 210097, China.
*Author to whom correspondence should be addressed.
Abstract
The paper deals with a nonlinear equation in one-dimensional space, of which the nonlinearity appears both in source term and the Neumann boundary condition. Firstly, we proved that the solution of problem (1.1) quenches in finite time and the only quenching point is x = 0 if the initial data is appropriate. Then we established the corresponding quenching rate of the solution.
Keywords: Nonlinear parabolic equation, quenching time, quenching rate, nonlinear boundary flux