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Global Solution of the System of Wave and Klein-Gordon Equations.

Vladimir Georgiev — 1990

Mathematische Zeitschrift

Resolvent estimates and the decay of the solution to the wave equation with potential

Vladimir Georgiev — 2001

Journées équations aux dérivées partielles

We prove a weighted $L^{\infty}$ estimate for the solution to the linear wave equation with a smooth positive time independent potential. The proof is based on application of generalized Fourier transform for the perturbed Laplace operator and a finite dependence domain argument. We apply this estimate to prove the existence of global small data solution to supercritical semilinear wave equations with potential.

Inverse scattering problem for the Maxwell equations outside moving body

Vladimir Georgiev — 1989

Annales de l'I.H.P. Physique théorique

$L^{\infty} - L^{2}$ weighted estimate for the wave equation with potential

Vladimir Georgiev; Nicola Visciglia — 2003

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We consider a potential type perturbation of the three dimensional wave equation and we establish a dispersive estimate for the associated propagator. The main estimate is proved under the assumption that the potential $V \geq 0$ satisfies $|V (x)| \leq \frac{C}{{(1 + |x|)}^{2 + ϵ_{0}}},$ where $ϵ_{0} > 0$ .

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Currently displaying 1 – 9 of 9

Global Solution of the System of Wave and Klein-Gordon Equations.

Resolvent estimates and the decay of the solution to the wave equation with potential

Inverse scattering problem for the Maxwell equations outside moving body

$L^{\infty} - L^{2}$ weighted estimate for the wave equation with potential

On Lipschitz continuity of the solution map for two-dimensional wave maps

Global existence of low regularity solutions of non-linear wave equations.

Strichartz Estimates for the Schrödinger Equation with small Magnetic Potential

RAGE theorem for power bounded operators and decay of local energy for moving obstacles

Solitary waves for Maxwell-Schrödinger equations.