Abstract
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 self-similar solutions which generalize Barenblatt profiles—the well-known solutions of the classical porous medium equation.
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Communicated by L. Saint-Raymond
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Biler, P., Imbert, C. & Karch, G. The Nonlocal Porous Medium Equation: Barenblatt Profiles and Other Weak Solutions. Arch Rational Mech Anal 215, 497–529 (2015). https://doi.org/10.1007/s00205-014-0786-1
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DOI: https://doi.org/10.1007/s00205-014-0786-1