DOIAbstract
AbstractWe study positive solutions of a fast diffusion equation in a bounded interval with a nonlinear Neumann boundary condition,ut=(um−1ux)x(x,t)∈(0,L)×(0,T),(um−1ux)(0,t)=um(0,t),t∈(0,T),(um−1ux)(L,t)=0,t∈(0,T),u(x,0)=u0(x),x∈[0,L],where m<0. Every positive solution quenches in a finite time. We prove that the quenching rate is not always the natural one given by homogeneity, but sometimes faster. We also study the quenching set, the asymptotic behaviour close to the quenching time and the possible continuation after that
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