4 papers
Existence of Complementary and Variational Weak Solutions to Obstacle Problems for a Quasilinear Wave Equation
João Paulo Dias, Wladimir Neves, José Francisco Rodrigues
We prove the existence of weak solutions for the one obstacle problem associated with a class of quasilinear wave equations in one space dimension, extending previous results obtai…
On short wave-long wave interactions\\ in the relativistic context: Application to the Relativistic Euler Equations
João Paulo Dias, Hermano Frid
In this paper we introduce a model of relativistic short wave-long wave interaction where the short waves are described by the massless -dimensional Thirring model of nonlinea…
On a coupled system of a Ginzburg-Landau equation with a quasilinear conservation law
João-Paulo Dias, Filipe Oliveira, Hugo Tavares
We study the Cauchy problem for a coupled system of a complex Ginzburg-Landau equation with a quasilinear conservation law $$ \left\{\begin{array}{rlll} e^{-iθ}u_t&=&u_{xx}-|u|^2u-…
On a quasilinear non-local Benney System
João-Paulo Dias, Filipe Oliveira
We study the quasilinear non-local Benney System $$\left\{\begin{array}{llll} iu_t+u_{xx}=|u|^2u+buv\\ v_t+a(\int_{\mathbf{R}^+}v^2dx)v_x=-b(|u|^2)_x,\quad (x,t)\in\mathbf{R}^+\tim…