Related papers: Nonlocal Cauchy problems for wave equations and ap…

For the Cauchy problem for an operator differential equation of the form $y'(z) = Ay(z)$, where $A$ is a closed linear operator on a Banach space over the completion of an algebraic closure of the field of $p$-adic numbers, a criterion of…

In this work we will consider integral equations defined on the whole real line and look for solutions which satisfy some certain kind of asymptotic behavior. To do that, we will define a suitable Banach space which, to the best of our…

The scalar wave equation in Kasner spacetime is solved, first for a particular choice of Kasner parameters, by relating the integrand in the wave packet to the Bessel functions. An alternative integral representation is also displayed,…

The Cauchy problem for two dimensional difference wave operators is considered with potentials and initial data supported in a bounded region. The large time asymptotic behavior of solutions is obtained. In contrast to the continuous case…

We show that blow up of solutions with arbitrary positive initial energy of the Cauchy problem for the abstract wacve eqation of the form $Pu_{tt}+Au=F(u) \ (*)$ in a Hilbert space, where $P,A$ are positive linear operators and $F(\cdot)$…

I describe a new algorithm for solving nonlinear wave equations. In this approach, evolution takes place on characteristic hypersurfaces. The algorithm is directly applicable to electromagnetic, Yang-Mills and gravitational fields and other…

Inspired by the work of Burq and Tzvetkov (Invent. math. 173(2008), 449-475.), firstly, we construct the local strong solution to the cubic nonlinear wave equation with random data for a large set of initial data in $H^{s}(M)$ with $s\geq…

The purpose of this note is to prove the existence of a conformal scattering operator for the cubic defocusing wave equation on a non-stationary background. The proof essentially relies on solving the characteristic initial value problem by…

We study the Cauchy problem for a quasilinear wave equation with low-regularity data. A space-time $L^2$ estimate for the variable coefficient wave equation plays a central role for this purpose. Assuming radial symmetry, we establish the…

In this paper, the integral initial value problems for Boussinesq type equations are studied. The equation include the general differential operators. The existence, uniqueness and regularity properties of solution of these problems are…

A problem of a wave identification is formulated. An example is considered in conditions of one-dimensional Cauchy problem for conventional string equation in matrix form and its inhomogeneous two-component version. The acoustic and…

We consider the global Cauchy problem for a two-component system of cubic semilinear wave equations in two space dimensions. We give a criterion for large time non-decay of the energy for small amplitude solutions in terms of the radiation…

We consider the Cauchy problem for wave equations with unbounded damping coefficients in the whole space. For a general class of unbounded damping coefficients, we derive uniform total energy decay estimates together with a unique existence…

The existence of solutions to Cauchy type problems of linear Riemann-Liouville fractional differential equations with variable coefficients is considered in a space of integrable functions. First, we consider the existence and uniqueness of…

We consider radial solutions to the Cauchy problem for the linear wave equation with a small short-range electromagnetic potential (the "square version" of the massless Dirac equation with a potential) and zero initial data. We prove two a…

Given a linear closed but not necessarily densely defined operator $A$ on a Banach space $E$ with nonempty resolvent set and a multivalued map $F\colon I\times E\map E$ with weakly sequentially closed graph, we consider the…

A fully non-linear kinetic Boltzmann equation for anyons and large initial data is studied in a periodic 1d setting. Strong L1 solutions are obtained for the Cauchy problem. The main results concern global existence, uniqueness, and…

We investigate inverse problems in the determination of leading coefficients for nonlocal parabolic operators, by knowing the corresponding Cauchy data in the exterior space-time domain. The key contribution is that we reduce nonlocal…

In this paper we are concerned with a nonlocal system to model the propagation of internal waves in a two-layer interface problem with rigid lid assumption and under a Boussinesq regime for both fluids. The main goal is to investigate…

The $m$-point nonlocal problem for the first order differential equation with an operator coefficient in a Banach space $X$ is considered. An exponentially convergent algorithm is proposed and justified provided that the operator…