We prove the existence of a Radon measure-valued solution for a class of nonlinear degenerate parabolic equations with a "logarithmic diffusion" when the initial datum u (0) is a bounded Radon measure, and we study the regularity of these solutions. In particular, we prove that a regularizing effect appears if the initial datum is diffused with respect to the "C (2)-capacity" since in this case the solution becomes a summable function. Finally, we study the uniqueness of these measure-valued solutions.
Measure-valued solutions of nonlinear parabolic equations with "logarithmic diffusion" / Orsina, Luigi; Porzio, Maria Michaela; F., Smarrazzo. - In: JOURNAL OF EVOLUTION EQUATIONS. - ISSN 1424-3199. - STAMPA. - 15:(2015), pp. 609-645. [10.1007/s00028-015-0275-5]
Measure-valued solutions of nonlinear parabolic equations with "logarithmic diffusion"
ORSINA, Luigi;PORZIO, Maria Michaela;
2015
Abstract
We prove the existence of a Radon measure-valued solution for a class of nonlinear degenerate parabolic equations with a "logarithmic diffusion" when the initial datum u (0) is a bounded Radon measure, and we study the regularity of these solutions. In particular, we prove that a regularizing effect appears if the initial datum is diffused with respect to the "C (2)-capacity" since in this case the solution becomes a summable function. Finally, we study the uniqueness of these measure-valued solutions.File | Dimensione | Formato | |
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