We consider a Riemann problem for the shallow water system u_ t+\big (v+\textstyle 1 2 u^
2\big) _ x= 0 ut+(v+ 1 2 u 2) x= 0, v_ t+\big (u+ uv\big) _ x= 0 vt+(u+ uv) x= 0 and evaluate all …

The present paper studies the interaction of Dirac δ-waves in models ruled by the nonlinear
Klein-Gordon equation utt− c 2 uxx= ϕ (u), where c> 0 is a real number and ϕ is an entire …

The present paper concerns the study of a Riemann problem for the system, with a one
dimensional space variable. We consider φ an entire function that takes real values on the …

This article studies a Riemann problem for the so-called “p-system” ut− vx= 0, vt−[σ (u)] x= 0,
which rules one-dimensional isentropic thermoelastic media. Such study is made using a …

The present paper concerns the system ut+[ϕ (u)] x= 0, vt+[ψ (u) v] x= 0 having distributions
as initial conditions. Under certain conditions, and supposing ϕ, ψ: ℝ→ ℝ functions, we …

Both propagation and collision behavior of δ′ waves in a model of three partial differential
equations are investigated. These are Cauchy problems for this model with initial values …

Newton's second law is applied to study the motion of a particle subjected to a time
dependent impulsive force containing a Dirac delta distribution. Within this setting, we prove …

In this paper, we prove that the model known as the zero pressure gas dynamic system with
certain singular measures as initial conditions may develop waves defined by distributions …

This paper studies a Riemann problem for the isentropic Euler equations and addresses two
gaps in the literature concerning positive pressures. Such study is made using a product of …

In the present paper we study, strictly within distribution theory, a one-dimensional
pressureless gas Euler system with a delta measure and a step function as initial conditions …