Related papers: Generalized Strichartz Estimates on Perturbed Wave…
We consider the Cauchy problem for the defocusing power type nonlinear wave equation in $(1+3)$-dimensions for energy subcritical powers $p$ in the range $3 < p< 5$. We prove that any solution is global-in-time and scatters to free waves in…
Wave propagation in curved tubular domains is considered. A general version of Webster's equation is derived from the scattering passive wave equation. More precisely, it is shown that planar averages of a sufficiently smooth solution of…
In this paper, we consider the Cauchy problem for semi-linear wave equations with structural damping term $\nu (-\Delta)^2 u_t$, where $\nu >0$ is a constant. As being mentioned in [8,10], the linear principal part brings both the diffusion…
It is well-known that the critical exponent for semilinear damped wave equations is Fujita exponent when the damping is effective. Lai, Takamura and Wakasa in 2017 have obtained a blow-up result not only for super-Fujita exponent but also…
We consider a semiclassical approximation for the time evolution of an originally gaussian wave packet in terms of complex trajectories. We also derive additional approximations replacing the complex trajectories by real ones. These yield…
This paper concerns estimates of the lifespan of solutions to the semilinear damped wave equation. We give upper estimates of the lifespan for the semilinear damped wave equation with variable coefficients in all space dimensions.
Some black hole mimickers, as well as black strings and other higher-dimensional spacetimes, exhibit stable light rings-regions where light or high-frequency gravitational waves can be trapped. In these regions, linear perturbations decay…
We consider the sharp Strichartz estimate for the wave equation on $\mathbb R^{1+5}$ in the energy space, due to Bez and Rogers. We show that it can be refined by adding a term proportional to the distance from the set of maximisers, in the…
An unconstrained, non-linearly elastic, semi-infinite solid is maintained in a state of large static plane strain. A power-law relation between the pre-stretches is assumed and it is shown that this assumption is well-motivated physically…
In this paper, we study the orbital stability of standing waves for one-dimensional nonlinear Schr\"odinger equations with potentials. We show that the standing waves are orbitally stable for all frequencies in the $L^{2}$- subcritical and…
This is the first in a series Of papers in which we initiate the study Of very rough solutions to the initial value problem for the Einstein Vacuum equations expressed relative to wave coordinates. By very rough we mean solutions which…
We prove decay estimates for solutions to non-isotropic linear systems of wave equations. The defining feature of these estimates is that they depend only on the commutation properties of the system with the scaling vector field. As…
An isotropic elastic half space is prestrained so that two of the principal axes of strain lie in the bounding plane, which itself remains free of traction. The material is subject to an isotropic constraint of arbitrary nature. A surface…
We present an elementary approach to prove restriction theorems for particular surfaces for which the Tomas-Stein theorem does not apply, which in turn provide short proofs for well-known Strichartz estimates for associated PDEs. The method…
In this article we consider variable coefficient, time-dependent wave equations. Using phase space methods we construct outgoing parametrices and prove Strichartz-type estimates globally in time. This is done in the context of C^2 metrics…
In this article, we are interested in studying the Cauchy problems for nonlinear damped wave equations and their systems on a weighted graph. Our main purpose is two-fold, namely, under certain conditions for volume growth of a ball and the…
We show that degenerate horizons exhibit a new trapping effect. Specifically, we obtain a non-degenerate Morawetz estimate for the wave equation in the domain of outer communications of extremal Reissner-Nordstrom up to and including the…
We study the dispersive properties of the wave equation associated with the shifted Laplace-Beltrami operator on Damek-Ricci spaces, and deduce Strichartz estimates for a large family of admissible pairs. As an application, we obtain global…
In this paper, we study the long-time existence result for small data solutions of quasilinear wave equations exterior to star-shaped regions in two space dimensions. The key novelty is that we establish a Morawetz type energy estimate for…
We prove almost global existence for semilinear wave equations outside of nontrapping obstacles. We use the vector field method, but only use the generators of translations and Euclidean rotations. Our method exploits 1/r decay of wave…