Related papers: The floating-body problem: an integro-differential…

We study the two-dimensional problem of propagation of linear water waves in deep water in the presence of a submerged body. Under some geometrical requirements, we derive an explicit bound for the solution depending on the domain and the…

Diffusion of a penetrating liquid in a polymeric material does not often satisfy the classical diffusion equations and requires taking relaxational (viscoelastic) properties of the polymer into account. We investigate a boundary value…

In the first of two papers, we study the initial boundary-value problem that underlies the theory of the Boltzmann equation for general non-spherical hard particles. In this work, for two congruent ellipses and for a large class of…

We derive and analyse well-posed boundary conditions for the linear shallow water wave equation. The analysis is based on the energy method and it identifies the number, location and form of the boundary conditions so that the initial…

We study a free boundary problem on the lattice whose scaling limit is a harmonic free boundary problem with a discontinuous Hamiltonian. We find an explicit formula for the Hamiltonian, prove the solutions are unique, and prove that the…

Large-scale simulations of the wave equation in electromagnetism, seismology, and acoustics, can be solved efficiently by finite difference methods. The accuracy of these numerical solutions usually depends on the minimization of…

This paper is concerned with the mathematical analysis of time-dependent fluid-solid interaction problem associated with a bounded elastic body immersed in a homogeneous air or fluid above a local rough surface. We reformulate the unbounded…

This paper considers to the problems of diffraction of electromagnetic waves on a half-plane, which has a finite inclusion in the form of a Lipschitz curve. The diffraction problem formulated as boundary value problem for Helmholtz…

In this paper, we consider the scattering of a plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in three dimensions. Based on the Helmholtz decomposition, the elastic scattering problem is reduced to a…

Evolution PDEs for dispersive waves are considered in both linear and nonlinear integrable cases, and initial-boundary value problems associated with them are formulated in spectral space. A method of solution is presented, which is based…

We study an integro-differential equation that describes the slow erosion of granular flow. The equation is a first order non-linear conservation law where the flux function includes an integral term. We show that there exist unique…

The problem of choice of boundary conditions are discussed for the case of numerical integration of the shallow water equations on a substantially irregular relief. In modeling of unsteady surface water flows has a dynamic boundary…

By employing a novel generalization of the inverse scattering transform method known as the unified transform or Fokas method, it can be shown that the solution of certain physically significant boundary value problems for the elliptic…

We study the initial-boundary value problem for a nonlinear wave equation given by u_{tt}-u_{xx}+\int_{0}^{t}k(t-s)u_{xx}(s)ds+ u_{t}^{q-2}u_{t}=f(x,t,u) , 0 < x < 1, 0 < t < T, u_{x}(0,t)=u(0,t), u_{x}(1,t)+\eta u(1,t)=g(t),…

The impact of a wedge-shaped body on the free surface of a weightless inviscid incompressible liquid is considered. Both symmetrical and unsymmetrical entries at constant velocity are dealt with. The differential problem corresponds to the…

Here we consider the problem of small oscillations of a rotating inviscid incompressible fluid. From a mathematical point of view, new exact solutions to the two-dimensional Poincar\'e-Sobolev equation in a class of domains including…

In this paper, new boundary differential equations for the two-dimensional exterior scattering problem have been derived. It has been shown that the Helmholtz equation can be reduced to an inhomogeneous Bessel's equation in a body-fitted…

We consider an inverse boundary value problem for a semilinear wave equation on a time-dependent Lorentzian manifold with time-like boundary. The time-dependent coefficients of the nonlinear terms can be recovered in the interior from the…

We consider a control system describing the interaction of water waves with a partially immersed rigid body constraint to move only in the vertical direction. The fluid is modeled by the shallow water equations. The control signal is a…

In this paper, we study the initial boundary value problem for the nonlinear wave equation with combined power-type nonlinearities with variable coefficients. The global behavior of the solutions with non-positive and sub-critical energy is…