In this paper, we study two systems with a time-variable coefficient and general time-gradually-degenerate damping. More explicitly, we construct the Riemann solutions to the time-variable coefficient Zeldovich approximation and time-variable …
In this work, we have expanded upon the (local) semi-discrete Lagrangian–Eulerian method initially introduced in Abreu et al. (2022) to approximate a specific class of multi-dimensional scalar conservation laws with nonlocal flux, referred to as the …
In this paper, we study the Riemann problem for a general variable coefficient Burgers equation with time-dependent damping. We use a nonlinear time-dependent viscosity equation with a similarity variable. Thus, when the viscosity goes to zero, we …
In this paper, we apply the method given in the paper “Zero relaxation time limits to a hydrodynamic model of two carrier types for semiconductors” (Mathematische Annalen, 2022, 382: 1031–1046) to study the Cauchy problem for a one dimensional …
In this paper we study a new property for the Glimm potential introduced by L. Caravenna [3]. This new property enable us to study scalar conservation laws with a particular source term called linear damping. By the operator splitting method joined …
In this work, we construct and analyze a new fully discrete Lagrangian-Eulerian numerical method for the treatment of dynamics of conservation laws with nonlocal flux and influence of the source term in the solution. The scheme is based on the …
In this paper, we show the local well-posedness for the Cauchy problem for the equation of the Nagumo type in this equation (1) in the Sobolev spaces $H^s(\mathbb{R})$ . If $D0$, the local well-posedness is given for $s 1/2$ and for $s 3/2$ if …
Las leyes de conservación son generalmente usadas en modelos que involucran principios de conservación (leyes físicas), tales como conservación de masa, momento lineal y de energía. Algunos ejemplos importantes de tales sistemas se encuentran en …
In this paper, we propose a time-dependent viscous system and by using the vanishing viscosity method we show the existence of solutions for the Riemann problem to a particular 2x2 system of conservation laws with linear damping.
In this paper, we propose a time-dependent viscous system and by using the vanishing viscosity method we show the existence of delta shock solutions for a generalized zero-pressure gas dynamics system with linear damping.