Quenching of a semilinear diffusion equation with convection and reaction

• Main Authors: Qian Zhou, Yuanyuan Nie, Xu Zhou, Wei Guo
• Format: Article
• Language: English
• Published: Texas State University 2015-08-01
• Series: Electronic Journal of Differential Equations
• Subjects: Quenching; critical length
• Online Access: http://ejde.math.txstate.edu/Volumes/2015/208/abstr.html

This article concerns the quenching phenomenon of the solution to the Dirichlet problem of a semilinear diffusion equation with convection and reaction. It is shown that there exists a critical length for the spatial interval in the sense that the solution exists globally in time if the length of the spatial interval is less than this number while the solution quenches if the length is greater than this number. For the solution quenching at a finite time, we study the location of the quenching points and the blowing up of the derivative of the solution with respect to the time.