Abstract In this paper we investigate the small data global existence and pointwise decay of solutions to two systems coupled wave-Klein–Gordon equations in spatial dimensions. particular, consider critical (in sense time decay) semilinear nonlinearities for wave equation below-critical Klein–Gordon equation, a situation that has not been studied before context equations. An interesting feature...

A relativistic analogue of the quantum adiabatic approximation is developed for Klein-Gordon fields minimally coupled to electromagnetism, gravity and an arbitrary scalar potential. The corresponding adiabatic dynamical and geometrical phases are calculated. The method introduced in this paper avoids the use of an inner product on the space of solutions of the Klein-Gordon equation. Its practic...

The influence functional method of Feynman and Vernon is used to obtain a quantum master equation for a system subjected to a Lévy stable random force. The corresponding classical transport equations for the Wigner function are then derived, both in the limits of weak and strong friction. These are fractional extensions of the Klein-Kramers and the Smoluchowski equations. It is shown that the f...

We investigate the stability properties of strongly continuous semigroups generated by operators form $A-BB^\ast$, where $A$ is a generator contraction semigroup and $B$ possibly unbounded operator. Such systems arise naturally in study hyperbolic partial differential equations with damping on boundary or inside spatial domain. As our main results we present general sufficient conditions for no...

We prove the global well-posedness and we study the linear response for a system of two coupled equations composed of a Dirac equation for an infinite rank operator and a nonlinear wave or Klein-Gordon equation.