A boundary value problem for the wave equation.
A characteristic initial value problem for a strictly hyperbolic system.
A fixed point theorem for affine mappings and its application to elasticity theory
In this paper we obtain a general fixed point theorem for an affine mapping in Banach space. As an application of this theorem we study existence of periodic solutions to the equations of the linear elasticity theory.
A functional method applied to operator equations.
A general decay estimate for a finite memory thermoelastic Bresse system
This work considers a Bresse system with viscoelastic damping on the vertical displacement and heat conduction effect on the shear angle displacement. A general stability result with minimal condition on the relaxation function is obtained. The system under investigation, to the best of our knowledge, is new and has not been studied before in the literature. What is more interesting is the fact that our result holds without the imposition of the equal speed of wave propagation condition, and differentiation...
A hyperbolic problem with nonlinear second-order boundary damping.
A memory type boundary stabilization of a mildly damped wave equation.
A Method of Characteristics Solving the Initial-Boundary Value Problem of a Hyperbolic Differential Equation of Second Order.
A mixed problem for quasilinear impulsive hyperbolic equations with non stationary boundary and transmission conditions.
A mixed problem with only integral boundary conditions for a hyperbolic equation.
A new method to obtain decay rate estimates for dissipative systems
A new method to obtain decay rate estimates for dissipative systems with localized damping.
We consider the wave equation damped with a locally distributed nonlinear dissipation. We improve several earlier results of E. Zuazua and of M. Nakao in two directions: first, using the piecewise multiplier method introduced by K. Liu, we weaken the usual geometrical conditions on the localization of the damping. Then thanks to some new nonlinear integral inequalities, we eliminate the usual assumption on the polynomial growth of the feedback in zero and we show that the energy of the system decays...
A new method to obtain decay rate estimates for dissipative systems
We consider the wave equation damped with a boundary nonlinear velocity feedback p(u'). Under some geometrical conditions, we prove that the energy of the system decays to zero with an explicit decay rate estimate even if the function ρ has not a polynomial behavior in zero. This work extends some results of Nakao, Haraux, Zuazua and Komornik, who studied the case where the feedback has a polynomial behavior in zero and completes a result of Lasiecka and Tataru. The proof is based on the construction...
A nonexistence result for a nonlinear PDE with Robin condition.
A nonlinear wave equation with a nonlinear integral equation involving the boundary value.
A nonlocal mixed semilinear problem for second-order hyperbolic equations.
A scaled characteristics method for the asymptotic solution of weakly nonlinear wave equations.
A selfadjoint hyperbolic boundary-value problem.
A self-adjoint “simultaneous crossing of the axis”.
A stability estimate for a solution of the problem of determining the dielectric permittivity.