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Article
Open AccessOn the well-posedness of the Cauchy problem for the two-component peakon system in \(C^k\cap W^{k,1}\)
This study focuses on the Cauchy problem associated with the two-component peakon system featuring a cubic nonlinearity, constrained to the class ...
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Article
Open AccessA nonlocal Lagrangian traffic flow model and the zero-filter limit
In this study, we start from a Follow-the-Leaders model for traffic flow that is based on a weighted harmonic mean (in Lagrangian coordinates) of the downstream car density. This results in a nonlocal Lagrangi...
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Article
Numerical methods for conservation laws with rough flux
Finite volume methods are proposed for computing approximate pathwise entropy/kinetic solutions to conservation laws with flux functions driven by low-regularity paths. For a convex flux, it is demonstrated th...
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Chapter and Conference Paper
Some Wellposedness Results for the Ostrovsky–Hunter Equation
The Ostrovsky-Hunter equation provides a model for small-amplitude long waves in a rotating fluid of finite depth. It is a nonlinear evolution equation. In this paper the welposedness of the Cauchy problem and...
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Article
An error estimate for the finite difference approximation to degenerate convection–diffusion equations
We consider semi-discrete first-order finite difference schemes for a nonlinear degenerate convection–diffusion equations in one space dimension, and prove an L 1 error estimate. Precisely, we sho...
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Article
Identification of diffusion parameters in a nonlinear convection–diffusion equation using the augmented Lagrangian method
Numerical identification of diffusion parameters in a nonlinear convection–diffusion equation is studied. This partial differential equation arises as the saturation equation in the fractional flow formulation...
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Article
A family of numerical schemes for kinematic flows with discontinuous flux
Multiphase flows of suspensions and emulsions are frequently approximated by spatially one-dimensional kinematic models, in which the velocity of each species of the disperse phase is an explicitly given funct...
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Chapter and Conference Paper
Global Weak Solutions for a Shallow Water Equation
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Chapter and Conference Paper
A Hyperbolic-Elliptic Model for Coupled Well-Porous Media Flow
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Article
Convergence Rates for Semi-Discrete Splitting Approximations for Degenerate Parabolic Equations with Source Terms
We study a semi-discrete splitting method for computing approximate viscosity solutions of the initial value problem for a class of nonlinear degenerate parabolic equations with source terms. It is fairly sta...
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Article
Monotone difference approximations for the simulation of clarifier-thickener units
Clarifier-thickener units treating ideal suspensions can be modeled as an initial-value problem for a nonconvex scalar conservation law whose flux depends on a vector of discontinuous parameters. This problem ...
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Article
Well-posedness in BV t and convergence of a difference scheme for continuous sedimentation in ideal clarifier-thickener units
We consider a scalar conservation law modeling the settling of particles in an ideal clarifier-thickener unit. The conservation law has a nonconvex flux which is spatially dependent on two discontinuous parame...
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Chapter and Conference Paper
Relaxation Schemes for Conservation Laws with Discontinuous Coefficients
We study relaxation schemes for conservation laws with discontinuous coefficients, and compare these numerically with an Engquist-Osher type scheme and with a front tracking method. If the coefficients are of ...
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Chapter and Conference Paper
On a Model for Continuous Sedimentation in Vessels with Discontinuous Cross-sectional Area
We study a clarifier-thickener unit considering that its cross-sectional area is not constant in both the clarification and the thickening zones. A mathematical model of sedimentation in such a vessel can be f...
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Article
Numerical Solution of the Polymer System by Front Tracking
The paper describes the application of front tracking to the polymer system, an example of a nonstrictly hyperbolic system. Front tracking computes piecewise constant approximations based on approximate Rieman...
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Chapter and Conference Paper
A Continuous Dependence Result for Nonlinear Degenerate Parabolic Equations with Spatially Dependent Flux Function
We study entropy solutions of nonlinear degenerate parabolic equations of form,where k(x) is a vector-valued function and f(u),A(u) are scalar functions. We prove a result concerning the continuous dependence ...
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Chapter and Conference Paper
On the Convergence Rate of Operator Splitting for Weakly Coupled Systems of Hamilton-Jacobi Equations
Assuming existence and uniqueness of bounded Lipschitz continuous viscosity solutions to the initial value problem for weakly coupled systems of Hamilton-Jacobi equations, we establish a linearL¡ã¡ãconvergence ra...
