Multiple viscous solutions for systems of conservation laws

Stability of systems of viscous conservation laws

Finite Dimensional Representation of Solutions of Viscous Conservation Laws

On Zero Mass Solutions of Viscous Conservation Laws

In the paper, we consider the large time behavior of solutions to the convection-diffusion equation ut−∆u+∇·f(u) = 0 in IRn× [0,∞), where f(u) ∼ uq as u → 0. Under the assumption that q ≥ 1 + 1/(n + β) and the initial condition u0 satisfies: u0 ∈ L1(IRn), ∫ IRn u0(x) dx = 0, and ‖eu0‖L1(IRn) ≤ Ct−β/2 for fixed β ∈ (0, 1), all t > 0, and a constant C, we show that the L1-norm of the solution to ...

A Subcell Resolution Method for Viscous Systems of Conservation Laws

We consider the generalization of scalar subcell resolution schemes to systems of viscous conservation laws. For this purpose we use a weakly nonlinear geometrical optics approximation for parabolic perturbations of hyperbolic conservation laws and the Roe-type field by field decomposition. Computations of the reactive Navier-Stokes equations are presented as an application.

Viscous Conservation Laws, Part I: Scalar Laws

Viscous conservation laws are the basic models for the dissipative phenomena. We aim at a systematic presentation of the basic ideas for the quantitative study of the nonlinear waves for viscous conservation laws. The present paper concentrates on the scalar laws; an upcoming Part II will deal with the systems. The basic ideas for scalar viscous conservation laws originated from two sources: th...