A fractional porous medium equation |
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| Authors: | Arturo de Pablo Fernando Quirós Ana Rodríguez Juan Luis Vázquez |
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| Institution: | aDepartamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés, Spain;bDepartamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain;cDepartamento de Matemática, ETS Arquitectura, Universidad Politécnica de Madrid, 28040 Madrid, Spain |
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| Abstract: | We develop a theory of existence, uniqueness and regularity for the following porous medium equation with fractional diffusion, with m>m?=(N−1)/N, N?1 and f∈L1(RN). An L1-contraction semigroup is constructed and the continuous dependence on data and exponent is established. Nonnegative solutions are proved to be continuous and strictly positive for all x∈RN, t>0. |
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| Keywords: | MSC: 26A33 35K55 |
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