Related papers: Evolution equations on time-dependent intervals
In this work we study partial differential equations defined in a domain that moves in time according to the flow of a given ordinary differential equation, starting out of a given initial domain. We first derive a formulation for a…
We study initial-boundary value problems for linear evolution equations of arbitrary spatial order, subject to arbitrary linear boundary conditions and posed on a rectangular 1-space, 1-time domain. We give a new characterisation of the…
This paper is concerned with the initial-boundary value problem for an evolutionary variational inequality complying with three intrinsic properties: complete irreversibility, unilateral equilibrium of an energy and an energy conservation…
Boundary value problems for integrable nonlinear evolution PDEs formulated on the finite interval can be analyzed by the unified method introduced by one of the authors and used extensively in the literature. The implementation of this…
We consider the problem of existence of a solution $u$ to $\partial_t u-\partial_{xx} u = 0$ in $(0,T)\times\mathbb{R}_+$ subject to the boundary condition $-u_x(t,0)+g(u(t,0))=\mu$ on $(0,T)$ where $\mu$ is a measure on $(0,T)$ and $g$ a…
In this paper we consider the initial boundary value problem (IBVP) for the nonlinear biharmonic Schr\"odinger equation posed on a bounded interval $(0,L)$ with non-homogeneous Navier or Dirichlet boundary conditions, respectively. For…
In the present article, we study the diffusion equations with fractional time derivatives. The aim of this paper is to investigate the best possible regularity for the initial value/boundary value problems with non-homogeneous Dirichlet…
Boundary value problems for the nonlinear Schrodinger equation on the half line in laboratory coordinates are considered. A class of boundary conditions that lead to linearizable problems is identified by introducing appropriate extensions…
A class of inverse problems for a heat equation with involution perturbation is considered using four different boundary conditions, namely, Dirichlet, Neumann, periodic and anti-periodic boundary conditions. Proved theorems on existence…
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…
A numerical method for the Dirichlet initial boundary value problem for the elastic equation in the exterior and unbounded region of a smooth closed simply connected 2-dimensional domain, is proposed and investigated. This method is based…
We consider the problem of numerically approximating the solutions to a partial differential equation (PDE) when there is insufficient information to determine a unique solution. Our main example is the Poisson boundary value problem, when…
A finite element based computational scheme is developed and employed to assess a duality based variational approach to the solution of the linear heat and transport PDE in one space dimension and time, and the nonlinear system of ODEs of…
A definition of invariance in Lie's sense for a boundary value problem (BVP) with the basic evolution differential equations is proposed. A problem of group classification at a wide class of BVPs parameterized by arbitrary elements is…
We examine an infinite, linear system of ordinary differential equations that models the evolution of fragmenting clusters, where each cluster is assumed to be composed of identical units. In contrast to previous investigations into such…
In his deep and prolific investigations of heat diffusion, Lam\'e was led to the investigation of the eigenvalues and eigenfunctions of the Laplace operator in an equilateral triangle. In particular he derived explicit results for the…
The main objective of this paper is analysis of the initial-boundary value problems for the linear time-fractional diffusion equations with a uniformly elliptic spatial differential operator of the second order and the Caputo type…
We provide a formulation of the initial boundary value problem for Friedrich's extended conformal Einstein field equations in which boundary data is prescribed on a timelike hypersurface located at a finite position in the spacetime. Our…
The time-fractional diffusion equation is considered, where the time derivative is either of Caputo or Riemann-Liouville type. The solution of a general initial-boundary value problem with time-dependent boundary conditions over bounded and…
We present a framework for recovering/approximating unknown time-dependent partial differential equation (PDE) using its solution data. Instead of identifying the terms in the underlying PDE, we seek to approximate the evolution operator of…