A linear difference scheme for dissipative symmetric regularized long wave equations with damping term.
A new conservative difference scheme for the general Rosenau-RLW equation.
A nonlinear boundary value problem for a system of hyperbolic partial differential equations.
Application of Moser's method to a certain type of evolution equations
Application of Rothe's method to perturbed linear hyperbolic equations and variational inequalities
Blowup of solutions for evolution equations with nonlinear damping.
Cauchy's problem for Bach's equations of general relativity.
Construction de solutions singulières pour des équations aux dérivées partielles non linéaires
Espaces de Sobolev et équations hyperboliques sur des variétés riemanniennes
Existence and analyticity of lump solutions for generalized Benney-Luke equations.
Existence and asymptotic behaviour for a degenerate Kirchhoff -Carrier model with viscosity and nonlinear boundary conditions.
The present paper studies the existence and uniqueness of global solutions and decay rates to a given nonlinear hyperbolic problem.
Existence and asymptotic stability of solutions for hyperbolic differential inclusions with a source term.
Existence and non-existence of global solutions for nonlinear hyperbolic equations of higher order
The existence and uniqueness of classical global solution and blow up of non-global solution to the first boundary value problem and the second boundary value problem for the equation are proved. Finally, the results of the above problem are applied to the equation arising from nonlinear waves in elastic rods
Existence and stability results of nonlinear higher-order wave equation with a nonlinear source term and a delay term
We consider the initial-boundary value problem for a nonlinear higher-order nonlinear hyperbolic equation in a bounded domain. The existence of global weak solutions for this problem is established by using the potential well theory combined with Faedo-Galarkin method. We also established the asymptotic behavior of global solutions as by applying the Lyapunov method.
Existence and uniform decay for a nonlinear beam equation with nonlinearity of Kirchhoff type in domains with moving boundary.
Existence of solutions of the Darboux problem for partial differential equations in Banach spaces
Existence, uniqueness and stabilization for a nonlinear plate system with nonlinear damping
Gerbes singulières et singularités du problème de Cauchy hyperbolique
Global attractor for the perturbed viscous Cahn-Hilliard equation
We consider the initial-boundary value problem for the perturbed viscous Cahn-Hilliard equation in space dimension n ≤ 3. Applying semigroup theory, we formulate this problem as an abstract evolutionary equation with a sectorial operator in the main part. We show that the semigroup generated by this problem admits a global attractor in the phase space (H²(Ω)∩ H¹₀(Ω)) × L²(Ω) and characterize its structure.
Global Classical Solutions of Nonlinear Wave Equations.