Abstract
Here we introduce a new notion of renormalized solution to nonlinear parabolic problems with general measure data whose model is (\[\left\{ {\begin{array}{*{20}{c}} {{u_t} - {\Delta _p}u = \mu \,in(0,T) \times \Omega ,}\\ {u = {u_0}\,on\{ 0\} \times \Omega }\\ {u = 0\,on(0,T) \times \delta \Omega } \end{array}} \right.\]) for any, possibly singular, nonnegative bounded measure μ. We prove existence of such a solutions and we discuss their main properties.
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Petitta, F., Porretta, A. On the Notion of Renormalized Solution to Nonlinear Parabolic Equations with General Measure Data. J Elliptic Parabol Equ 1, 201–214 (2015). https://doi.org/10.1007/BF03377376
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DOI: https://doi.org/10.1007/BF03377376