Existence of solutions of quenching problems
Daniel Philips · Applicable Analysis · 1987
We find continuous nonnegative solutions of the equation Δu - ut = u-pX({u>0}) when 0<p< 1 for the Cauchy problem on IRn and the initial value-Dirichlet problem on bounded domains. The motivation for this work comes from reaction diffusion models, Δu - ut − f(∊,u), where for , is smooth and . Such a limiting process is used here.