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Energy and large time estimates for nonlinear porous medium ow with nonlocal pressure in RN



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Dao, Nguyen Anh and Díaz, Ildefonso Jesús (2020) Energy and large time estimates for nonlinear porous medium ow with nonlocal pressure in RN. Archive for Rational Mechanics and Analysis, 238 . pp. 299-345. ISSN 0003-9527

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Official URL: https://doi.org/10.1007/s00205-020-01543-1


We study the general family of nonlinear evolution equations of fractional diffusive type [delta]u-div(|u|m1[nabla]([delta]-s||u||m2-1u|= f. Such type of nonlocal equationsare related to the porous medium equations with a fractional Laplacian pressure.Our study concerns the case in which the ow takes place in the whole space. We consider m1;m2 > 0, and s 2 (0; 1), and prove existence of weak solutions. Moreover, when f _ 0 we obtain the Lp-L1 decay estimates of solutions, for p _ 1. Besides, we also investigate the _nite time extinction of solution. Our results improve the recent papers in the literature.

Item Type:Article
Uncontrolled Keywords:Quasilinear parabolic equations; Flows in porous media; Parabolic systems
Subjects:Sciences > Physics > Mathematical physics
Sciences > Mathematics > Differential equations
ID Code:73985
Deposited On:22 Jul 2022 09:13
Last Modified:03 Aug 2022 10:08

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