Existence and Asymptotic Behavior for a Singular Parabolic Equation


We prove global existence of nonnegative solutions to the singular parabolic equation ut−∆u+χ{u>0}(−u−β+λf(u)) = 0 in a smooth bounded domain Ω ⊂ RN with zero Dirichlet boundary condition and initial condition u0 ∈ C(Ω), u0 ≥ 0. In some cases we are also able to treat u0 ∈ L∞(Ω). Then we show that if the stationary problem admits no solution which is… (More)