estimates for the wave equation and applications
Laplace transform pairs of N-dimensions and second order linear partial differential equations with constant coefficients.
Large time behaviour of the solutions to some nonlinear evolution equations
Le noyau de l'équation des ondes sur une variété riemannienne compacte comme intégrale de chemins
Le problème mixte des équations des ondes et applications
Les singularités des fonctions spectrales sur une variété riemannienne infiniment aplatie
Les singularités du noyau de l'opérateur de diffusion pour des obstacles non-convexes
L’existence d’une solution classique d’une éqéaire dans (Communication préalable)
L'intégrale de Riemann-Liouville et le problème de Cauchy pour l'équation des ondes
L∞-Norm minimal control of the wave equation: on the weakness of the bang-bang principle
For optimal control problems with ordinary differential equations where the -norm of the control is minimized, often bang-bang principles hold. For systems that are governed by a hyperbolic partial differential equation, the situation is different: even if a weak form of the bang-bang principle still holds for the wave equation, it implies no restriction on the form of the optimal control. To illustrate that for the Dirichlet boundary control of the wave equation in general not even feasible...
Local energy decay for several evolution equations on asymptotically euclidean manifolds
Let be a long range metric perturbation of the Euclidean Laplacian on , . We prove local energy decay for the solutions of the wave, Klein-Gordon and Schrödinger equations associated to . The problem is decomposed in a low and high frequency analysis. For the high energy part, we assume a non trapping condition. For low (resp. high) frequencies we obtain a general result about the local energy decay for the group where has a suitable development at zero (resp. infinity).
Lp-Abschätzungen und klassische Lösungen für nichtlineare Wellengleichungen. I.
Lp-Decacy Rates for Homogeneous Wave-Equations.
Lp-estimates for the wave equation on the Heisenberg group.
Let £ denote the sub-Laplacian on the Heisenberg group Hm. We prove that ei√£ / (1 - £)α/2 extends to a bounded operator on Lp(Hm), for 1 ≤ p ≤ ∞, when α > (d - 1) |1/p - 1/2|.
Matematika hudebních nástrojů
Mathematical and numerical modelling of piezoelectric sensors
The present work aims at proposing a rigorous analysis of the mathematical and numerical modelling of ultrasonic piezoelectric sensors. This includes the well-posedness of the final model, the rigorous justification of the underlying approximation and the design and analysis of numerical methods. More precisely, we first justify mathematically the classical quasi-static approximation that reduces the electric unknowns to a scalar electric potential. We next justify the reduction of the computation...
Mathematical and numerical modelling of piezoelectric sensors
The present work aims at proposing a rigorous analysis of the mathematical and numerical modelling of ultrasonic piezoelectric sensors. This includes the well-posedness of the final model, the rigorous justification of the underlying approximation and the design and analysis of numerical methods. More precisely, we first justify mathematically the classical quasi-static approximation that reduces the electric unknowns to a scalar electric potential. We next justify the reduction of the computation...
Mathematical and numerical modelling of piezoelectric sensors
The present work aims at proposing a rigorous analysis of the mathematical and numerical modelling of ultrasonic piezoelectric sensors. This includes the well-posedness of the final model, the rigorous justification of the underlying approximation and the design and analysis of numerical methods. More precisely, we first justify mathematically the classical quasi-static approximation that reduces the electric unknowns to a scalar electric potential. We next justify the reduction of the computation...
Maximizers for the Strichartz Inequality
We compute explicitly the best constants and, by solving some functional equations, we find all maximizers for homogeneous Strichartz estimates for the Schrödinger equation and for the wave equation in the cases when the Lebesgue exponent is an even integer.
Mémoire sur l'intégration des équations aux différences partielles de la Physique mathématique.