| Abstract: |
| Initial-boundary value problems for nonlinear parabolic equations having Radon measures as initial data have been widely investigated, looking for solutions which for positive times take values in some function space. On the other hand, in order to overcome the lack of existence of function-valued solutions in the most degenerate cases, recently several results have been obtained in the direction of a theory for Radon measure-valued solutions
In this talk, we study existence of Radon measure-valued solutions to the homogeneous Dirichlet initial-boundary value problem for a class of parabolic equations without strong coercivity. The notion of solution is natural, since it is obtained by a suitable approximation of the initial measure. Qualitative properties of solutions concerning the evolution of their singular part are discussed, as well as conditions (depending on the initial data and on the strength of degeneracy of the diffusivity at infinity) under which the constructed solutions are in fact function-valued or not. |
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