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We study the solutions of a parabolic system of heat equations coupled at the boundary through a nonlinear flux. We characterize in terms of the parameters involved when non-simultaneous quenching may appear. Moreover, if quenching is non-simultaneous we find the quenching rate, which surprisingly depends on the flux associated to the other component.
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… (More)
We study the behaviour of nonnegative solutions of the reaction-diffusion equation u t = (u m) xx + a(x)u p in R × (0, T), u(x, 0) = u 0 (x) in R. The model contains a porous medium diffusion term with exponent m > 1, and a localized reaction a(x)u p where p > 0 and a(x) ≥ 0 is a compactly supported function. We investigate the existence and behaviour… (More)