On the Cauchy problem for a general fractional porous medium equation with variable density

By Fabio Punzo, Gabriele Terrone. 2013

51 citations recorded by the source corpus.

We study the well-posedness of the Cauchy problem for a fractional porous medium equation with a varying density. We establish existence of weak energy solutions; uniqueness and nonuniqueness is studied as well, according with the behavior of the density at infinity.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2ea6404fdf09894d0a535159a118ad5579f1e625

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In Applied Mathematics

1. Juan Luis V'azquez
2. Matteo Bonforte
3. G. Grillo
4. A. Audrito
5. Yannick Sire
6. Razvan Gabriel Iagar
7. Alessio Figalli
8. Jean Dolbeault

In Mathematical Physics

1. Juan Luis V'azquez
2. Matteo Bonforte
3. G. Grillo
4. A. Audrito
5. Razvan Gabriel Iagar

Citations in the corpus

• Quantitative local and global a priori estimates for fractional nonlinear diffusion equations (2012, background): “on 7; understanding the asymptotic behaviour of the fractional KPP equation [35]; dealing with nonlocal symmetrization problems [41]; or uniqueness issues for the fractional PME with variable density [33]. Outline of the paper and main results. First, some preliminary information on case divisions. ”
• An Existence Theorem for Fractional Hybrid Differential Inclusions of Hadamard Type with Dirichlet Boundary Conditions (2014, unknown): “Much of the work on fractional differential equations involves either Riemann-Liouville derivative or Caputo derivative; for instance, see [4–33] and the references therein.”