Related papers: Mathematical aspects of numerical solution of hype…
We introduce a new wave formulation for the relativistic Euler equations with vacuum boundary conditions that consists of a system of non-linear wave equations in divergence form with a combination of acoustic and Dirichlet boundary…
The behavior of sufficiently regular solutions to semilinear hyperbolic equations has attracted a great deal of attention in the past decades, concerning local/global existence, finite time blow-up, critical exponents, and propagation of…
In this paper we present a treatment of hypersingular integral equations, which have relevant applications in many problems of wave dynamics, elasticity and fluid mechanics with mixed boundary conditions. The main goal of the present work…
In recent years, several numerical methods for solving the unique continuation problem for the wave equation in a homogeneous medium with given data on the lateral boundary of the space-time cylinder have been proposed. This problem enjoys…
We propose a simple algebraic method for constructing exact solutions of equations of two-dimensional hydrodynamics of an incompressible fluid. The problem reduces to consecutively solving three linear partial differential equations for a…
This paper is devoted to confront two different approaches to the problem of dynam-ical perfect plasticity. Interpreting this model as a constrained boundary value Friedrichs' system enables one to derive admissible hyperbolic boundary…
Shock waves, vorticity waves, and entropy waves are fundamental discontinuity waves in nature and arise in supersonic or transonic gas flow, or from a very sudden release (explosion) of chemical, nuclear, electrical, radiation, or…
The article summarizes the studies of wave fields in structured non-equilibrium media describing by means of nonlocal hydrodynamic models. Due to the symmetry properties of models, we derived the invariant wave solutions satisfying…
We study solutions to nonlinear hyperbolic systems with fully nonlinear relaxation terms in the limit of, both, infinitely stiff relaxation and arbitrary late time. In this limit, the dynamics is governed by effective systems of parabolic…
In this paper we will consider the peridynamic equation of motion which is described by a second order in time partial integro-differential equation. This equation has recently received great attention in several fields of Engineering…
We present a computational analysis of a 2$\times$2 hyperbolic system of balance laws whose solutions exhibit complex nonlinear behavior. Traveling-wave solutions of the system are shown to undergo a series of bifurcations as a parameter in…
We discuss selected topics of current research interest in the theory of dynamical systems, with emphasis on dimension theory, multifractal analysis, and quantitative recurrence. The topics include the quantitative versus the qualitative…
We consider numerical methods for linear parabolic equations in one spatial dimension having piecewise constant diffusion coefficients defined by a one parameter family of interface conditions at the discontinuity. We construct immersed…
We consider the coupling between the equations of motion of an inviscid compressible fluid in space with an objective Cattaneo-type extension for the heat flux. These equations are written in quasilinear form and we determine which of the…
In the following paper we will consider Navier-Stokes problem and it's interpretation by hyperbolic waves, focusing on wave propagation. We will begin with solution for linear waves, then present problem for non-linear waves. Later we will…
Kinetic relations are required in order to characterize nonclassical undercompressive shock waves and formulate a well-posed initial value problem for nonlinear hyperbolic systems of conservation laws. Such nonclassical waves arise in weak…
The development of a coherent conceptual basis for the treatment of non-linear microscopic phenomena, such as, hydrodynamic interaction, finite extensibility, excluded volume and internal viscosity, in molecular theories of dilute polymer…
The present study concerns the numerical homogenization of second order hyperbolic equations in non-divergence form, where the model problem includes a rapidly oscillating coefficient function. These small scales influence the large scale…
In this paper, the authors propose a numerical method to compute the solution of a nonlinear reaction-diffusion problem in the case of HS-regime. The initial condition is a nonnegative function with compact support. The problem is split in…
Time-periodic weak solutions for a coupled hyperbolic-parabolic system are obtained. A linear heat and wave equation are considered on two respective $d$-dimensional spatial domains that share a common $(d-1)$-dimensional interface…