Complete Blow-up and Avalanche Formation for a Parabolic System with Non-Simultaneous Blow-up Articles uri icon

publication date

  • August 2010

start page

  • 659

end page

  • 679

issue

  • 3

volume

  • 10

International Standard Serial Number (ISSN)

  • 1536-1365

abstract

  • We study the possibility of defining a nontrivial continuation after the blow-uptime for a system of two heat equations with a nonlinear coupling at the boundary. It turns out that any possible continuation that verify a maximum principle is identically infinity after the blow-up time, that is, both components blow up completely. We also analyze the propagation of the singularity to the whole space, the avalanche, when blow-up is non-simultaneous.