On the Cauchy problem for a general fractional porous medium equation with variable density. (English) Zbl 1284.35005

Summary: We study the well-posedness of the Cauchy problem for a fractional porous medium equation with a varying density \({\rho}>0\). We establish existence of weak energy solutions; uniqueness and nonuniqueness is studied as well, according to the behavior of \({\rho}\) at infinity.


35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
35E15 Initial value problems for PDEs and systems of PDEs with constant coefficients
35K55 Nonlinear parabolic equations
35R11 Fractional partial differential equations
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