Nonlocal porous medium equation: Barenblatt profiles and other weak solutions
نویسنده
چکیده
A degenerate nonlinear nonlocal evolution equation is considered; it can be understood as a porous medium equation whose pressure law is nonlinear and nonlocal. We show the existence of sign changing weak solutions to the corresponding Cauchy problem. Moreover, we construct explicit compactly supported selfsimilar solutions which generalize Barenblatt profiles — the well-known solutions of the classical porous medium equation.
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