Abstract
Here we give an existence and uniqueness result of a renormalized solution for a class of nonlinear parabolic equations \(\displaystyle {\partial b(u) \over \partial t} - \mathrm{div}(a(x,t,\nabla u))+\mathrm{div}(\Phi (x,t, u))=\mu \), where the right side is a measure data, b is a strictly increasing \(C^1\)-function, \(- \mathrm{div}(a(x,t,\nabla u))\) is a Leray–Lions type operator with growth \(|\nabla u|^{p-1}\) in \(\nabla u\) and \(\Phi (x,t, u)\) is a nonlinear lower order term.
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Funding was provided by Bouajaja (Grant no. 1975).
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Bouajaja, A., Redwane, H. & Marah, A. Existence and Uniqueness of Renormalized Solutions to Nonlinear Parabolic Equations with Lower Order Term and Diffuse Measure Data. Mediterr. J. Math. 15, 178 (2018). https://doi.org/10.1007/s00009-018-1223-8
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DOI: https://doi.org/10.1007/s00009-018-1223-8