On the notion of renormalized solution to nonlinear parabolic equations with general measure data

AbstractHere 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.