A kinetic approach to comparison properties for degenerate parabolic-hyperbolic equations with boundary conditions

DOI10.1016/j.jde.2006.07.008zbMath1105.35004OpenAlexW2039028467MaRDI QIDQ860753

Kazuo Kobayasi

Publication date: 9 January 2007

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2006.07.008

zbMATH Keywords

comparison theorementropy sub- and supersolutionkinetic traces

Mathematics Subject Classification ID

PDEs of mixed type (35M10) Degenerate parabolic equations (35K65) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Related Items (10)

An \(L^1\)-theory for scalar conservation laws with multiplicative noise on a periodic domain ⋮ The boundary degeneracy theory of a strongly degenerate parabolic equation ⋮ The Cauchy problem for a class of nonlinear degenerate parabolic-hyperbolic equations ⋮ Ergodicity for stochastic conservation laws with multiplicative noise ⋮ Well-posedness for stochastic scalar conservation laws with the initial-boundary condition ⋮ Uniqueness and existence for anisotropic degenerate parabolic equations with boundary conditions on a bounded rectangle ⋮ A stochastic conservation law with nonhomogeneous Dirichlet boundary conditions ⋮ Applications of the kinetic formulation for scalar conservation laws with a zero-flux type boundary condition ⋮ Positive solutions of quasilinear parabolic systems with Dirichlet boundary condition ⋮ Viscosity solutions of a class of degenerate quasilinear parabolic equations with Dirichlet boundary condition

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonhomogeneous Dirichlet problems for degenerate parabolic-hyperbolic equations
• On a nonlinear degenerate parabolic equation in infiltration or evaporation through a porous medium
• Uniqueness and error estimates in first order quasilinear conservation laws via the kinetic entropy defect measure
• Entropy solutions for nonlinear degenerate problems
• Extended divergence-measure fields and the Euler equations for gas dynamics
• The equivalence of weak solutions and entropy solutions of nonlinear degenerate second-order equations
• An error estimate for the parabolic approximation of multidimensional scalar conservation laws with boundary conditions
• Mathematical analysis of nonlinear models of petrol engineering
• First order quasilinear equations with boundary conditions
• A Kinetic Formulation of Multidimensional Scalar Conservation Laws and Related Equations
• On the uniqueness of the solution of the evolution dam problem
• Entropy Formulation for Parabolic Degenerate Equations with General Dirichlet Boundary Conditions and Application to the Convergence of FV Methods
• A Kinetic Formulation for Multidimensional Scalar Conservation Laws with Boundary Conditions and Applications
• Strong traces for solutions of multidimensional scalar conservation laws

This page was built for publication: A kinetic approach to comparison properties for degenerate parabolic-hyperbolic equations with boundary conditions