Related papers: Behavior of Solutions to An Initial Boundary Value…
We propose a numerical method to solve an inverse source problem of computing the initial condition of hyperbolic equations from the measurements of Cauchy data. This problem arises in thermo- and photo- acoustic tomography in a bounded…
In this paper we consider the classical initial value problem for the bosonic membrane in light cone gauge. A Hamiltonian reduction gives a system with one constraint, the area preserving constraint. The Hamiltonian evolution equations…
Linearisation is often used as a first step in the analysis of nonlinear initial boundary value problems. The linearisation procedure frequently results in a confusing contradiction where the nonlinear problem conserves energy and has an…
In this paper, some initial-boundary-value problems for the time-fractional diffusion equation are first considered in open bounded n-dimensional domains. In particular, the maximum principle well-known for the PDEs of elliptic and…
We consider self-similar approximations of nonlinear hyperbolic systems in one space dimension with Riemann initial data and general diffusion matrix. We assume that the matrix of the system is strictly hyperbolic and the diffusion matrix…
This paper presents the generalized Fourier series solution for the longitudinal vibrations of a bar subjected to viscous boundary conditions at each end. The model of the system produces a non-selfadjoint eigenvalue problem which does not…
We consider boundary value problems of the first and third kind for the diffusionwave equation. By using the method of energy inequalities, we find a priori estimates for the solutions of these boundary value problems.
A new method is proposed to improve the numeri- cal simulation of time dependent problems when the initial and boundary data are not compatible. Unlike earlier methods limited to space dimension one, this method can be used for any space…
In this work we study linear Maxwell equations with time- and space-dependent matrix-valued permittivity and permeability on domains with a perfectly conducting boundary. This leads to an initial boundary value problem for a first order…
Einstein's system of equations in the ADM decomposition involves two subsystems of equations: evolution equations and constraint equations. For numerical relativity, one typically solves the constraint equations only on the initial time…
We consider a second order singularly perturbed boundary value problem, of reaction-convection-diffusion type with two small parameters, and the approximation of its solution by the $hp$ version of the Finite Element Method on the so-called…
Under consideration is the hyperbolic relaxation of a semilinear reaction-diffusion equation on a bounded domain, subject to a dynamic boundary condition. We also consider the limit parabolic problem with the same dynamic boundary…
We investigate how the scaling behavior of finite systems at magnetic first-order transitions (FOTs) with relaxational dynamics changes in correspondence of various boundary conditions. As a theoretical laboratory we consider the…
In this paper we focus on the Cahn-Hilliard equation with dynamic boundary conditions, by adding two hyperbolic relaxation terms to the system. We verify that the energy of the total system is decreasing with time. By adding two…
In this paper we apply a scaling invariance analysis to reduce a class of parabolic moving boundary problems to free boundary problems governed by ordinary differential equations. As well known free boundary problems are always non-linear…
Variational methods play an important role in the study of quantum many-body problems, both in the flavor of classical variational principles based on tensor networks as well as of quantum variational principles in near-term quantum…
We introduce a new approach to constructing analytic solutions of the linear PDEs describing elastodynamics. This approach is illustrated for the case of a homogeneous isotropic half-plane body satisfying arbitrary initial conditions and…
The aim of this paper is to draw attention to an interesting semilinear parabolic equation that arose when describing the chaotic dynamics of a polymer molecule in a liquid. This equation is nonlocal in time and contains a term, called the…
This work explores the solvability of a sixth-order Cahn--Hilliard equation with an inertial term, which serves as a relaxation of a higher-order variant of the classical Cahn--Hilliard equation. The equation includes a source term that…
This paper studies the dynamical behavior of classical solutions to a hyperbolic system of balance laws, derived from a chemotaxis model with logarithmic sensitivity, subject to time-dependent boundary conditions. It is shown that under…