2022/01/17 by Philippe Laurençot, Laurençot, Philippe, Bogdan-Vasile Matioc +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP
paper · pdf · doi:10.48550/arxiv.2201.06479
arXiv admin note: text overlap with arXiv:2110.01234
arxiv created 2022/01/17 · arxiv updated 2022/01/19
Bounded weak solutions are constructed for a degenerate parabolic system with a full diffusion matrix, which is a generalized version of the thin film Muskat system. Boundedness is achieved with the help of a sequence (En)n≥ 2 of Liapunov functionals such that En is equivalent to the Ln-norm for each n ≥ 2 and En1/n controls the L_∞-norm in the limit n→∞. Weak solutions are built by a compactness approach, special care being needed in the construction of the approximation in order to preserve the availability of the above-mentioned Liapunov functionals.