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

dc.contributor.authorDao, Nguyen Anh
dc.contributor.authorDíaz, Ildefonso Jesús
dc.description.abstractWe 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.
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
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dc.journal.titleArchive for Rational Mechanics and Analysis
dc.rights.accessRightsopen access
dc.subject.keywordQuasilinear parabolic equations
dc.subject.keywordFlows in porous media
dc.subject.keywordParabolic systems
dc.subject.ucmFísica matemática
dc.subject.ucmEcuaciones diferenciales
dc.subject.unesco1202.07 Ecuaciones en Diferencias
dc.titleEnergy and large time estimates for nonlinear porous medium ow with nonlocal pressure in RN
dc.typejournal article
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