Related papers: Infinite energy solutions for weakly damped quinti…
For a damped wave (or Klein-Gordon) equation on a bounded domain, with a focusing power-like nonlinearity satisfying some growth conditions, we prove that a global solution is bounded in the energy space, uniformly in time. Our result…
We establish both global existence and decay properties for solutions with small data for a general class of coupled system of tensorial quasilinear hyperbolic wave equations in three space dimensions, that covers the dynamical Einstein…
We consider damped wave equations with a potential and rotational inertia terms. We study the Cauchy problem for this model in the one dimensional Euclidean space and we obtain fast energy decay and L^2-decay of the solution itself as time…
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.
We present a new method of investigating the so-called quasi-linear strongly damped wave equations $$ \partial_t^2u-\gamma\partial_t\Delta_x u-\Delta_x u+f(u)= \nabla_x\cdot \phi'(\nabla_x u)+g $$ in bounded 3D domains. This method allows…
We present general results on exponential decay of finite energy solutions to stationary nonlinear Schr\"odinger equations.
The main objective of this manuscript is to investigate the global behavior of the solutions to the viscoelastic wave equation with a linear memory term of Boltzmann type, and a nonlinear damping modeling friction, as well as a…
We consider several models of nonlinear wave equations subject to very strong damping and quasi-periodic external forcing. This is a singular perturbation, since the damping is not the highest order term. We study the existence of response…
We prove the existence of weak solutions in the space of energy for a class of non-linear Schroedinger equations in the presence of a external rough magnetic potential. Under our assumptions it is not possible to study the problem by means…
A detailed investigation is presented of a simple unidirectional finite-energy solution of the 3D wave equation. Its asymptotics as a spatial point runs to infinity with the wave propagations speed is a standard spherical wave as z < 0,…
This short note serves as an introduction to the papers arXiv:1711.01651 and arXiv:1711.04486 by Maekawa, Miura and Prange. These two works deal with the existence of mild solutions on the one hand and local energy weak solutions on the…
In this paper we analyze the large-time behavior of weak solutions to polytropic fluid models possibly including quantum and capillary effects. Formal a priori estimates show that the density of solutions to these systems should disperse…
We show that a large class of supersymmetric solutions to the low-energy effective field theory of heterotic string theory compactified on a seven torus can have finite energy, which we compute. The mechanism by which these solutions are…
In this paper we study the global existence of small data solutions to the Cauchy problem for the semilinear wave equation with scale-invariant damping. We obtain estimates for the solution and its energy with the same decay rate of the…
We study the large time behavior of solutions to the semilinear wave equation with space-dependent damping and absorbing nonlinearity in the whole space or exterior domains. Our result shows how the amplitude of the damping coefficient, the…
We consider the quintic, focusing semilinear wave equation on $\mathbb{R}^{1+3}$, in the radially symmetric setting, and construct infinite time blow-up, relaxation, and intermediate types of solutions. More precisely, we first define an…
In this paper we study a class of nonlinear Schr\"odinger equations which admit families of small solitary wave solutions. We consider solutions which are small in the energy space $H^1$, and decompose them into solitary wave and dispersive…
This article gives an energy decay result for small data solutions to a class of semilinear wave equations in two space dimensions possessing weakly dissipative structure relevant to the Agemi condition.
We consider finite-energy solutions to the defocusing nonlinear wave equation in two dimensional space. We prove that almost all energy moves to the infinity at almost the light speed as time tends to infinity. In addition, the…
We examine the solutions of the semilinear wave equation, and, in particular, of the $\varphi ^p$ model of quantum field theory in the curved space-time. More exactly, for $1< p<4$ we prove that solution of the massless self-interacting…