Partial Differential Equations

In this work, we expand on the weak asymptotic analysis originally proposed in Abreu et al. (2024) for the investigation of scalar equations and systems of conservation laws, extending it to encompass scalar equations with nonlocal fluxes. …

In this paper, we study the Riemann solutions for two systems: the nonsymmetric Keyfitz–Kranzer system and the pressureless system, both characterized by a time-dependent Coulomb-like friction term. Our analysis identifies two types of Riemann …

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 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 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 $s1/2$ and for $s3/2$ 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 …