Quasilinear Parabolic Equations Associated with Semilinear Parabolic Equations

Abstract

We formulate a quasilinear parabolic equation describing the behavior of the global-in-time solution to a semilinear parabolic equation. We study this equation in accordance with the blow-up and quenching patterns of the solution to the original semilinear parabolic equation. This quasilinear equation is new in the theory of partial differential equations and presents several difficulties for mathematical analysis. Two approaches are examined: functional analysis and a viscosity solution.

Keywords

• semilinear parabolic equation
• quasilinear parabolic equation
• blowup pattern