Well-posedness for non-isotropic degenerate parabolic-hyperbolic equations

By Gui-Qiang G. Chen, Benoit Perthame. 2003

227 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fa883dc69f1c7dd71e22472497f877b2d5e3bae9

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. Martina Hofmanov'a
2. Julien Vovelle
3. Gui-Qiang G. Chen
4. Arnaud Debussche
5. Yachun Li
6. Qin Wang
7. Kenneth Hvistendahl Karlsen
8. Benoit Perthame

In Computational Theory and Mathematics

1. Gui-Qiang G. Chen
2. Yachun Li
3. Qin Wang
4. Martina Hofmanov'a
5. Kenneth Hvistendahl Karlsen
6. Julien Vovelle
7. Arnaud Debussche
8. Benoit Perthame

In Mathematical Physics

1. Martina Hofmanov'a
2. Yachun Li
3. Qin Wang
4. Kenneth Hvistendahl Karlsen
5. Arnaud Debussche
6. Julien Vovelle
7. Eitan Tadmor
8. Gui-Qiang G. Chen

Citations in the corpus

• QUASILINEAR ANISOTROPIC DEGENERATE PARABOLIC EQUATIONS WITH TIME-SPACE DEPENDENT DIFFUSION COEFFICIENTS (2005, methodology): “The uniqueness of entropy solutions in L(1) was proved in [16] by developing a kinetic formulation and using the regularization by convolution.”
• Degenerate parabolic stochastic partial differential equations (2013, background): “P201/10/0752. already been studied in the case of hyperbolic scalar conservation laws in both deterministic (see e.g. [16], [19], [20], [22], or [23] for a general presentation) and stochastic setting (see [6]); and also in the case of deterministic degenerate parabolic equations of second-order…”
• Renormalized entropy solutions of homogeneous Dirichlet problems for quasilinear anisotropic degenerate parabolic-hyperbolic equations (2012, methodology): “[32] B. Perthame, P.E. Souganidis, Dissipative and entropy solutions to non-isotropic degenerate parabolic balance laws, Arch.”
• Degenerate parabolic stochastic partial differential equations: Quasilinear case (2013, methodology): “This concept was first introduced by Lions, Perthame, Tadmor [22] for deterministic hyperbolic conservation laws.”
• Mathematical tools for kinetic equations (2004, background): “Another application is to uniqueness of the solution [102], [35].”
• Velocity averaging, kinetic formulations, and regularizing effects in quasi‐linear PDEs (2007, background): “The solutions sought by Chen and Perthame in [11], ρ ∈ L∞, require that their corresponding distribution function χρ satisfy (4.”