## 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.

### MSC:

 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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