Partial Differential Equations

Cauchy problem for isothermal system in a general nozzle with space-dependent friction

In this paper, we study the Cauchy problem of the isothermal system in a general nozzle with space-dependent friction α(x). First, by using the maximum principle, we obtain the uniform bound ρδ,ε,τ≤M, |mδ,ε,τ|≤M, independent of the time, of the …

Interaction of delta shock waves for a nonsymmetric Keyfitz–Kranzer system of conservation laws

In this work, the mechanism for the formation of the delta shock wave is analyzed to deal with interaction of delta shock waves and contact discontinuities for a system of Keyfitz–Kranzer type by means of analysis and solutions of Riemann problems. A …

On the Cauchy problem for Aw-Rascle system with linear damping

The existence of global BV solutions for the Aw-Rascle system with linear damping is considered. In order to get approximate solutions we consider the system in Lagrangian coordinates, then by using the wave front tracking method coupling with and …

Riemann Problem for a 2x2 Hyperbolic System with Linear Damping

In this paper, we study the Riemann problem for a 2x2 nonstrictly hyperbolic system with linear damping. We introduce the special time-dependent viscosity to obtain approximate solutions. Therefore, we solve the Riemann problem (1.1)–(1.2) by …

Lagrangian structure for two dimensional non-barotropic compressible fluids

We study the Lagrangian structure for weak solutions of two dimensional Navier–Stokes equations for a non-barotropic compressible fluid, i.e. we show the uniqueness of particle trajectories for two dimensional compressible fluids including the energy …

Generalized Riemann problem for a totally degenerate hyperbolic system

We consider the generalized Riemann problem for the Suliciu re- laxation system in Lagrangian coordinates and we calculate the first-order ex- pansion given by LeFloch and Raviart to verify our results, then we show the explicit solution for the …

Delta shock waves for a system of Keyfitz‐Kranzer type

This paper is concerned with a hyperbolic system of conservation laws of Keyfitz-Kranzer type. We show the existence of a delta shock wave solution using the vanishing viscosity method. The obtained solution satisfies the generalized Rankine-Hugoniot …

Lower Bounds for Possible Singular Solutions for the Navier–Stokes and Euler Equations Revisited

In this paper we give optimal lower bounds for the blow-up rate of the 𝐻˙𝑠(𝕋3)-norm, 1/252

Delta shock wave for a 3x3 hyperbolic system of conservation laws

We study the one-dimensional Riemann problem for a hyperbolic system of three conservation laws of Temple class. The system is a simplification of a recently proposed system of five conservations laws by Bouchut and Boyaval that models viscoelastic …

Regularity of Viscous Solutions for a Degenerate Non-linear Cauchy Problem

We consider the Cauchy problem for a class of nonlinear degenerate parabolic equation with forcing. By using the vanishing viscosity method it is possible to construct a generalized solution. Moreover, this solution is a Lipschitz function on the …