A UNIQUENESS CONDITION FOR NONLINEAR CONVECTION-DIFFUSION EQUATIONS WITH DISCONTINUOUS COEFFICIENTS
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Publication:3636283
DOI10.1142/S0219891609001794zbMath1180.35305MaRDI QIDQ3636283
Publication date: 30 June 2009
Published in: Journal of Hyperbolic Differential Equations (Search for Journal in Brave)
Degenerate parabolic equations (35K65) Hyperbolic conservation laws (35L65) PDEs with low regular coefficients and/or low regular data (35R05) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
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Cites Work
- Unnamed Item
- Solving the Buckley-Leverett equation with gravity in a heterogeneous porous medium
- Stability of conservation laws with discontinuous coefficients
- Well-posedness for a class of \(2\times 2\) conservation laws with \(\mathbb{L}^\infty\) data
- Well-posedness in \(BV_t\) and convergence of a difference scheme for continuous sedimentation in ideal clarifier-thickener units
- Convergence of the Lax-Friedrichs scheme and stability for conservation laws with a discontinuous space-time dependent flux
- A front tracking approach to a model of continuous sedimentation in ideal clarifier-thickener units
- Scalar conservation laws with discontinuous flux function. I: The viscous profile condition
- Scalar conservation laws with discontinuous flux function. II: On the stability of the viscous profiles
- Existence and stability of entropy solutions for a conservation law with discontinuous non-convex fluxes
- A regulator for continuous sedimentation in ideal clarifier-thickener units
- Operating charts for continuous sedimentation. IV: Limitations for control of dynamic behaviour
- Operating charts for continuous sedimentation. III: Control of step inputs
- Operating charts for continuous sedimentation. II: Step responses
- ANALYSIS AND APPROXIMATION OF A SCALAR CONSERVATION LAW WITH A FLUX FUNCTION WITH DISCONTINUOUS COEFFICIENTS
- OPTIMAL ENTROPY SOLUTIONS FOR CONSERVATION LAWS WITH DISCONTINUOUS FLUX-FUNCTIONS
- Convergence of Godunov type methods for a conservation law with a spatially varying discontinuous flux function
- Solution of the Cauchy Problem for a Conservation Law with a Discontinuous Flux Function
- Analysis and Approximation of Conservation Laws with Source Terms
- Monotone Difference Approximations Of BV Solutions To Degenerate Convection-Diffusion Equations
- Convergence of a Difference Scheme for Conservation Laws with a Discontinuous Flux
- Godunov-Type Methods for Conservation Laws with a Flux Function Discontinuous in Space
- Upwind difference approximations for degenerate parabolic convection-diffusion equations with a discontinuous coefficient
- ON A DIFFUSIVELY CORRECTED KINEMATIC-WAVE TRAFFIC FLOW MODEL WITH CHANGING ROAD SURFACE CONDITIONS
- On Scalar Conservation Laws with Point Source and Discontinuous Flux Function
- Convex conservation laws with discontinuous coefficients. existence, uniqueness and asymptotic behavior
- A conservation Law with Point Source and Discontinuous Flux Function Modelling Continuous Sedimentation
- Existence and Uniqueness of Entropy Solution of Scalar Conservation Laws with a Flux Function Involving Discontinuous Coefficients
- A Model of Continuous Sedimentation of Flocculated Suspensions in Clarifier-Thickener Units
- CAUCHY'S PROBLEM FOR DEGENERATE SECOND ORDER QUASILINEAR PARABOLIC EQUATIONS
- FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES
- Stability of a resonant system of conservation laws modeling polymer flow with gravitation
- Operating charts for continuous sedimentation. I: Control of steady states.
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