Abstract.
We consider the nonlinear heat equation (with Leray-Lions operators) on an open bounded subset of RN with Dirichlet homogeneous boundary conditions. The initial condition is in L1 and the right hand side is a smooth measure. We extend a previous notion of entropy solutions and prove that they coincide with the renormalized solutions.
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Droniou, J., Prignet, A. Equivalence between entropy and renormalized solutions for parabolic equations with smooth measure data. Nonlinear differ. equ. appl. 14, 181–205 (2007). https://doi.org/10.1007/s00030-007-5018-z
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DOI: https://doi.org/10.1007/s00030-007-5018-z