Existence and uniqueness of solutions of diffusion-absorption equations with general data
J. L. Vázquez, Magdalena Walias · Differential and Integral Equations · 1994
We study the nonlinear parabolic equation in the exponent range 1 0. We discuss several extensions, like existence of solutions with changing sign, and existence of solutions when the initial datum is a locally finite measure.We also consider the problem posed in an open subset of RN with infinite boundary data.Finally, we comment on extensions to other related equations of a more general form.Introduction.This paper studies the existence and uniqueness of solutions of the Cauchy ProblemThe constant a > 0 can be taken to be 1 without loss of generality.The initial data uo can be any nonnegative and locally integrable function in RN.No assumption has to be made on the behavior of u0 as x -too.Equation (0.1) is a simple and useful way of describing a process of diffusion (or thermal propagation) accompanied by absorption, in the case where the diffusivity (resp.thermal conductivity) and the absorption coefficient are assumed to be dependent on the concentration (resp.temperature) represented by u.There is an extensive literature devoted to the physical aspects and mathematical study of such problems, cf.Kalashnikov's survey paper [17] for a discussion of results and related literature.See also references below.Let us state our main results.First, we have existence and uniqueness of a solution.