Existence of global solutions to the Cauchy problem for the seminlinear dissipative wave equations.
Existence of global weak solutions to a symmetrically hyperbolic system with a source.
Existence of optimal controls for control systems governed by nonlinear partial differential equations
Existence of positive solutions for nonlinear boundary value problems in bounded domains of .
Existence of pseudo almost periodic solutions to some classes of partial hyperbolic evolution equations.
Existence of pullback attractors for the coupled suspension bridge equations.
Existence of quasilinear relaxation shock profiles in systems with characteristic velocities
We revisit the existence problem for shock profiles in quasilinear relaxation systems in the case that the velocity is a characteristic mode, implying that the profile ODE is degenerate. Our result states existence, with sharp rates of decay and distance from the Chapman–Enskog approximation, of small-amplitude quasilinear relaxation shocks. Our method of analysis follows the general approach used by Métivier and Zumbrun in the semilinear case, based on Chapman–Enskog expansion and the macro–micro...
Existence of solutions for a nonlinear hyperbolic-parabolic equation in a non-cylinder domain.
Existence of solutions for a variational unilateral system.
Existence of solutions for discontinuous hyperbolic partial differential equations in Banach algebras.
Existence of solutions for hyperbolic system of second order outside a domain.
Existence of solutions for one-dimensional wave equations with nonlocal conditions.
Existence of solutions of a second order abstract functional Cauchy problem with nonlocal conditions
We establish the existence of mild, strong, classical solutions for a class of second order abstract functional differential equations with nonlocal conditions.
Existence of solutions of nonlinear hyperbolic equations
Existence of solutions of the Darboux problem for partial differential equations in Banach spaces
Existence of solutions to a second order partial differential equation with nonlocal conditions.
Existence of solutions to generalized von Foerster equations with functional dependence
We prove the existence of solutions to a differential-functional system which describes a wide class of multi-component populations dependent on their past time and state densities and on their total size. Using two different types of the Hale operator, we incorporate in this model classical von Foerster-type equations as well as delays (past time dependence) and integrals (e.g. influence of a group of species).
Existence of solutions to microhyperbolic boundary value problems
Existence of solutions to nonlinear advection-diffusion equation applied to Burgers' equation using Sinc methods
This paper has two objectives. First, we prove the existence of solutions to the general advection-diffusion equation subject to a reasonably smooth initial condition. We investigate the behavior of the solution of these problems for large values of time. Secondly, a numerical scheme using the Sinc-Galerkin method is developed to approximate the solution of a simple model of turbulence, which is a special case of the advection-diffusion equation, known as Burgers' equation. The approximate solution...
Existence of weak solutions for abstract hyperbolic-parabolic equations.