Source-Type Solutions of Diffusion Equations with Nonlinear Convection
Guofu Lu · Chinese Annals of Mathematics · 2007
This paper is interested in the following equation u_t=u_(xx)+(u~n)_x with a measure as its initial conditions.If its initial datum is a Dirae measure,it is shown that there exists a critical value n=3 such that the existence and uniqueness of solutions of the problems as 0≤n3 and the nonexistence of solutions of the problems as n≥3 are true respectively.The author also studies the asymptotic behavior of its solution near (0,0) as 0≤n2 and similarity source-type solutions to the problems as n=2.