Quenching behavior and critical speed for a parabolic problem due to a moving nonlinear source

Abstract

This article investigates an initial–boundary value problem on the semi-infinite interval for a parabolic equation with a moving nonlinear source. The study presents criteria for both finite-time quenching and global existence of the solution. It is shown that there exists a critical speed v∗ for the nonlinear source, ensuring global existence of the solution when the speed of the moving nonlinear source is greater than or equal to v∗, while finite-time quenching occurs when the speed is smaller than v∗. The formula to calculate the critical speed v∗ is also provided for a special case.

Keywords

• Semilinear parabolic first-initial boundary value problem
• Moving nonlinear source
• Semi-infinite interval
• Single quenching point
• Global existence
• Finite time quenching