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We study a porous medium equation with dissipative and hyperdiffusive effects and no sign restrictions on the diffusion coefficient.
|||G. M. Coclite and L. di Ruvo, Existence results for the Kudryashov–Sinelshchikov–Olver equation, Proc. R. Soc. Edinb. Sect. A, 151 (2021), 425-450. doi: 10.1017/prm.2020.23.|
|||G. M. Coclite and L. di Ruvo, Well-posedness of the classical solution for the Kuramto–Sivashinsky equation with anisotropy effects, Z. Angew. Math. Phys., 72 (2021), Article number: 68. doi: 10.1007/s00033-021-01506-w.|
|||G. M. Coclite and L. di Ruvo, The porous medium equation with capillary pressure effects, Preprint.|
|||M. E. Taylor, Partial Differential Equations I. Basic Theory, vol. 115 of Applied Mathematical Sciences, 2nd edition, Springer, New York, 2011. doi: 10.1007/978-1-4419-7055-8.|
|||J. L. Vázquez, The Porous Medium Equation, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, Oxford, 2007.|