Asymptotic theory for weakly nonlinear wave equations in semi-infinite domains.
Asymptotics for some nonlinear damped wave equation : finite time convergence versus exponential decay results
Bifurcations near a double eigenvalue of the rectangular plate problem with a domain parametr
Blowup and asymptotic stability of weak solutions to wave equations with nonlinear degenerate damping and source terms.
Blow-up of solutions for an integro-differential equation with a nonlinear source.
Blowup of solutions of a nonlinear wave equation.
Blow-up of weak solutions for the semilinear wave equations with nonlinear boundary and interior sources and damping
We focus on the blow-up in finite time of weak solutions to the wave equation with interior and boundary nonlinear sources and dissipations. Our central interest is the relationship of the sources and damping terms to the behavior of solutions. We prove that under specific conditions relating the sources and the dissipations (namely p > m and k > m), weak solutions blow up in finite time.
Blow-up time of some nonlinear wave equations.
Boundary sentinels in cylindrical domains.
We study a model describing vibrations of a cylindrical domain with thickness e > 0. A characteristic of this model is that it contains pollution terms in the boundary data and missing terms in the initial data. The method of sentinels'' of J. L. Lions [7] is followed to construct a sentinel using the observed vibrations on the boundary. Such a sentinel, by construction, provides information on pollution terms independent of missing terms. This requires resolution of initial-boundary value...
Boundary value problems in time for wave equations on .
Bounded solutions of second order semicoercive evolution equations in a Hilbert space and of nonlinear telegraph equations.
Breakdown in finite time of solutions to a one-dimensional wave equation.
We consider a special type of a one-dimensional quasilinear wave equation wtt - phi (wt / wx) wxx = 0 in a bounded domain with Dirichlet boundary conditions and show that classical solutions blow up in finite time even for small initial data in some norm.
Cauchy problem for hyperbolic operators with triple characteristics of variable multiplicity
We study a class of third order hyperbolic operators in with triple characteristics on . We consider the case when the fundamental matrix of the principal symbol for has a couple of non vanishing real eigenvalues and is strictly hyperbolic for We prove that is strongly hyperbolic, that is the Cauchy problem for is well posed in for any lower order terms .
Comparison of exact and approximate causal solutions of a model curved-space wave equation
Comparison theorems for ultrahyperbolic equations.
Continuous dependence and general decay of solutions for a wave equation with a nonlinear memory term
We study existence, uniqueness, continuous dependence, general decay of solutions of an initial boundary value problem for a viscoelastic wave equation with strong damping and nonlinear memory term. At first, we state and prove a theorem involving local existence and uniqueness of a weak solution. Next, we establish a sufficient condition to get an estimate of the continuous dependence of the solution with respect to the kernel function and the nonlinear terms. Finally, under suitable conditions...
Control for hyperbolic equations
Control of the wave equation by time-dependent coefficient
We study an initial boundary-value problem for a wave equation with time-dependent sound speed. In the control problem, we wish to determine a sound-speed function which damps the vibration of the system. We consider the case where the sound speed can take on only two values, and propose a simple control law. We show that if the number of modes in the vibration is finite, and none of the eigenfrequencies are repeated, the proposed control law does lead to energy decay. We illustrate the rich behavior...
Control of the Wave Equation by Time-Dependent Coefficient
We study an initial boundary-value problem for a wave equation with time-dependent sound speed. In the control problem, we wish to determine a sound-speed function which damps the vibration of the system. We consider the case where the sound speed can take on only two values, and propose a simple control law. We show that if the number of modes in the vibration is finite, and none of the eigenfrequencies are repeated, the proposed control law does lead to energy decay. We illustrate the rich behavior of...
Contrôle de l'équation des ondes dans des ouverts comportant des coins