The Asymptotic Behaviour of the Solution of a Nonlinear Diffusion Equation
Carmen Cortázar, Manuel Elgueta · SIAM Journal on Mathematical Analysis · 1985
We prove that a generalized solution of a filtration equation of the form ${{\partial u} / {\partial t}} = ({\partial / {\partial x}})(\sigma (u){{\partial u} / {\partial x}})$, where $\lim _{s \to 0} ({{\sigma (s)} / {s^\lambda }}) = 1$, behaves asymptotically as the selfsimilar solution of ${{\partial u} / {\partial t}} = ({\partial / {\partial x}})(u^\lambda {{\partial u} / {\partial x}})$.