Quenching, global existence and blowup phenomena in heat transfer

2020/01/15 by Xianfa Song, Song, Xianfa
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Stability and Controllability of Differential Equations #math-ph #math.AP #math.MP

paper · pdf · doi:10.48550/arxiv.2001.07529

arxiv created 2020/01/15 · arxiv updated 2020/01/22

Abstract

Basing on the relations between a system of ODE and a system of parabolic equations, we establish some general theories in heat transfer about quenching, global existence and blowup phenomena, obtain the conditions(even watershed) on f(u,v), g(u,v), a(x) and b(x) which let the solution be global existence, quench or blow up, and estimate the bounds for blowup time and quenching time.

Related

• Blowup versus global in time existence of solutions for nonlinear heat equations
• The Blow-up Rate Estimates for a System of Heat Equations with Nonlinear Boundary Conditions
• Blow-up at space infinity for solutions of a system of non-autonomous semilinear heat equations
• Global existence and finite time blow-up for the heat flow of H-system with constant mean curvature
• The Quenching Problem in the Nonlinear Heat Equations