Existence of absorbing set for a nonlinear wave equation.
Existence of almost automorphic solutions to some classes of nonautonomous higher-order differential equations.
Existence of classical solutions and feedback stabilization for the flow in gas networks
We consider the flow of gas through pipelines controlled by a compressor station. Under a subsonic flow assumption we prove the existence of classical solutions for a given finite time interval. The existence result is used to construct Riemannian feedback laws and to prove a stabilization result for a coupled system of gas pipes with a compressor station. We introduce a Lyapunov function and prove exponential decay with respect to the L2-norm.
Existence of classical solutions and feedback stabilization for the flow in gas networks
We consider the flow of gas through pipelines controlled by a compressor station. Under a subsonic flow assumption we prove the existence of classical solutions for a given finite time interval. The existence result is used to construct Riemannian feedback laws and to prove a stabilization result for a coupled system of gas pipes with a compressor station. We introduce a Lyapunov function and prove exponential decay with respect to the L2-norm.
Existence of global solution of a nonlinear wave equation with short-range potential
Existence of global solutions of the Yang-Mills, Higgs and spinor field equations in dimensions
Existence of global solutions to a quasilinear wave equation with general nonlinear damping.
Existence of Global Solutions to Supercritical Semilinear Wave Equations
∗The author was partially supported by Alexander von Humboldt Foundation and the Contract MM-516 with the Bulgarian Ministry of Education, Science and Thechnology.In this work we study the existence of global solution to the semilinear wave equation (1.1) (∂2t − ∆)u = F(u), where F(u) = O(|u|^λ) near |u| = 0 and λ > 1. Here and below ∆ denotes the Laplace operator on R^n. The existence of solutions with small initial data, for the case of space dimensions n = 3 was studied by F. John in [13],...
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.