Abstract.
The aim of this paper is to study, for L 1-data, the absorption problem of parabolic type : \(u_t - {\rm div} a(u, Du) + \beta(x, u) \ni f\) with Dirichlet boundary conditions and initial conditions. Here a satisfies the classical Leray-Lions hypotheses and β(x, ·) is the subdifferential ∂j(x, ·), where j is a convex function such that j(·, 0) = 0. Existence and uniqueness of an entropy solution is established.
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Andreianov, B., Sbihi, K. & Wittbold, P. On uniqueness and existence of entropy solutions for a nonlinear parabolic problem with absorption. J. evol. equ. 8, 449–490 (2008). https://doi.org/10.1007/s00028-008-0365-8
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DOI: https://doi.org/10.1007/s00028-008-0365-8