The Porous Medium Equation: Mathematical Theory

By Juan Luis V'azquez. 2006

1,313 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/2e9fddf939f3e37ce9c8adc3d7c3108e795cac8a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Juan Luis V'azquez
2. Matteo Bonforte
3. A. Audrito
4. Alessio Figalli
5. Xavier Ros-Oton
6. Razvan Gabriel Iagar
7. D. Bianchi
8. A. G. Setti

In Computational Mechanics

1. A. Audrito
2. Matteo Bonforte
3. D. Bianchi
4. A. G. Setti
5. Michael Winkler
6. Lucio Boccardo
7. Nicola Bellomo
8. Alessio Figalli

In Computational Theory and Mathematics

1. Juan Luis V'azquez
2. Matteo Bonforte
3. A. Audrito
4. D. Bianchi
5. A. G. Setti
6. Giuseppe Viglialoro
7. Alessio Figalli
8. Razvan Gabriel Iagar

Citations in the corpus

• A degenerate chemotaxis system with flux limitation: Maximally extended solutions and absence of gradient blow-up (2016, background): “ations characterized by a finite propagation velocity. Intuitively, the answer is that phenomena with finite propagation velocity should be captured by an appropriate choice of nonlinear diffusion terms [31]. A conceivable approach leads to consider functions Du(u,v) and Dv(u,v) not only depending on u”
• Nonlinear Diffusion with Fractional Laplacian Operators (2012, methodology): “They can be seen as fractional-diffusion versions of the PME described above, [68], [67].”
• Existence and uniqueness of solutions to an aggregation equation with degenerate diffusion (2010, neutral): “For the wealth of information on the filtration equation and further references we refer to the book by Vazquez [37].”
• Gradient Estimates for the Porous Medium Equations on Riemannian Manifolds (2011, neutral): “6) see [1,10,13] and the references therein.”
• Renormalized entropy solutions of homogeneous Dirichlet problems for quasilinear anisotropic degenerate parabolic-hyperbolic equations (2012, background): “Degenerate parabolic–hyperbolic equations have been intensively studied in many important applications such as sedimentation–consolidation processes and two phase flows in porous media, see [13, 15,22] and the references cited therein.”
• Dirichlet problems with singular and gradient quadratic lower order terms (2008, background): “Such kind of problems has been studied in [33].”