相关论文: Singular solutions for a 2X2 system in nonconserva…
In this paper, we investigate the inverse quasi-variational inequality problem in finite-dimensional spaces. First, we introduce a second-order dynamical system whose trajectory converges exponentially to the solution of the inverse…
We construct examples of oscillating solutions with persistent oscillations for various hyperbolic-parabolic systems with singular diffusion matrices that appear in mechanics. These include, an example for the equations of nonlinear…
For hyperbolic first-order systems of linear partial differential equations (master equations), appearing in description of kinetic processes in physics, biology and chemistry we propose a new procedure to obtain their complete closed-form…
We revisit the theory of first-order quasilinear systems with diagonalizable principal part and only real eigenvalues, what is commonly referred to as strongly hyperbolic systems. We provide a self-contained and simple proof of local…
In this paper we discuss some remarkable properties of the autonomous system of 2 first-order Ordinary Differential Equations (ODEs), which equates the derivatives $\dot{x}_n(t)$ ($n = 1, 2$) of the 2 dependent variables $x_n(t)$ to the…
In this note we consider two different singular limits to hyperbolic system of conservation laws, namely the standard backward schemes for non linear semigroups and the semidiscrete scheme. Under the assumption that the rarefaction curve of…
This paper is devoted to the extension of the recently proposed conditional symmetry method to first order nonhomogeneous quasilinear systems which are equivalent to homogeneous systems through a locally invertible point transformation. We…
A detailed study of solutions to the first order partial differential equation H(x,y,z_x,z_y)=0, with special emphasis on the eikonal equation z_x^2+z_y^2=h(x,y), is made near points where the equation becomes singular in the sense that…
We consider solutions to the hyperbolic system of equations of ideal granular hydrodynamics with conserved mass, total energy and finite momentum of inertia and prove that these solutions generically lose the initial smoothness within a…
Second-order dynamical systems are important tools for solving optimization problems, and most of existing works in this field have focused on unconstrained optimization problems. In this paper, we propose an inertial primal-dual dynamical…
The paper deals with the decoupling problem of general quasilinear first order systems in two independent variables. We consider either the case of homogeneous and autonomous systems or the one of nonhomogeneous and/or nonautonomous…
We consider a focusing Davey-Stewartson system and construct the solution of the Cauchy problem in the possible presence of exceptional points (and/or curves).
In this paper, we propose an adaptive high-order method for hyperbolic systems of conservation laws. The proposed method is based on a dual formulation approach: Two numerical solutions, corresponding to conservative and nonconservative…
A method is given for solving an optimal H2 approximation problem for SISO linear time-invariant stable systems. The method, based on constructive algebra, guarantees that the global optimum is found; it does not involve any gradient-based…
We construct the solution of the Riemann problem for the shallow water equations with discontinuous topography. The system under consideration is non-strictly hyperbolic and does not admit a fully conservative form, and we establish the…
In an attempt to solve Maxwell's first order system of equations, starting from a given initial state, it is found that a consistent solution depending on the temporal evolution of the sources cannot be calculated. The well known retarded…
The existence and uniqueness of weak solutions is shown for a system related to the Willis model of elastodynamics. Both the whole space case and the case of a bounded smooth domain are studied. To this end the equations are reformulated as…
A unified general approach is presented for construction of solutions of the characteristic initial value problems for various integrable hyperbolic reductions of Einstein's equations for space-times with two commuting isometries in General…
The relativistic two-body system in (1+1)-dimensional quantum electrodynamics is studied. It is proved that the eigenvalue problem for the two-body Hamiltonian without the self-interaction terms reduces to the problem of solving an…
We cast the non--isentropic relativistic Euler system into a symmetric hyperbolic form. Such systems are very suited to treat initial value problems of hyperbolic type. We obtain this form by using the pressure $p$ and not the density…