Incomplete Quenching in a System of Heat Equations Coupled at the Boundary Articles uri icon

publication date

  • October 2008

start page

  • 145

end page

  • 154

issue

  • 1

volume

  • 346

International Standard Serial Number (ISSN)

  • 0022-247X

Electronic International Standard Serial Number (EISSN)

  • 1096-0813

abstract

  • In this paper we find a possible continuation for quenching solutions to a system of heat equations coupled at the boundary condition. This system exhibits simultaneous and non-simultaneous quenching. For non-simultaneous quenching our continuation is a solution of a parabolic problem with Neumann boundary conditions. We also give some results for simultaneous quenching and present some numerical experiments that suggest that the approximations are not uniformly bounded in this case.