Related papers: Initial-boundary value problem for distributed ord…
In this paper, we consider an initial boundary value problem for Maxwell's equations. For this hyperbolic type problem, we derive guaranteed and computable upper bounds for the difference between the exact solution and any pair of vector…
We consider the equations which describe polytropic one-dimensional flows of viscous compressible multifluids. We prove global existence and uniqueness of a solution to the initial-boundary value problem which corresponds to the flow in a…
This paper is concerned with the blow-up property of solutions to an initial boundary value problem for a reaction diffusion equation with special diffusion processes. It is shown, under certain conditions on the initial data, that the…
We study a local data inverse problem for the time-dependent Convection-Diffusion Equation (CDE) in a bounded domain where a part of the boundary is treated to be inaccessible. Up on assuming the inaccessible part to be flat, we seek for…
For $\nu,\nu_i,\mu_j\in(0,1)$, we analyze the semilinear integro-differential equation on the one-dimensional domain $\Omega=(a,b)$ in the unknown $u=u(x,t)$ \[…
We formulate the initial value problem for causal variational principles in the continuous setting on a compact metric space. The existence and uniqueness of solutions is analyzed. The results are illustrated by simple examples.
When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model, for example, the orders of the fractional derivative or the source term, are often unknown,…
We establish existence and uniqueness results for initial boundary value problems with nearly incompressible vector fields. We then apply our results to establish well-posedness of the initial-boundary value problem for the Keyfitz and…
There has been considerable recent interest in solving non-local equations of motion which contain an infinite number of derivatives. Here, focusing on inflation, we review how the problem can be reformulated as the question of finding…
We consider a fractional diffusion equations of order $\alpha\in(0,1)$ whose source term is singular in time: $(\partial_t^\alpha+A)u(x,t)=\mu(t)f(x)$, $(x,t)\in\Omega\times(0,T)$, where $\mu$ belongs to a Sobolev space of negative order.…
In the last 40 years the study of initial boundary value problem for the Korteweg-de Vries equation has had the attention of researchers from various research fields. In this note we present a review of the main results about this topic and…
We prove that, for a given spherically symmetric fluid distribution with tangential pressure on an initial spacelike hypersurface with a timelike boundary, there exists a unique, local in time solution to the Einstein equations in a…
In this article we address some issues related to the initial value problems for a rotating shallow water hyperbolic system of equations and the diffusive regularization of this system. For initial data close to the solution at rest, we…
In this article we study a class of generalised linear systems of difference equations with given boundary conditions and assume that the boundary value problem is non-consistent, i.e. it has infinite many or no solutions. We take into…
We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…
We consider the boundary crossing problem for time-homogeneous diffusions and general curvilinear boundaries. Bounds are derived for the approximation error of the one-sided (upper) boundary crossing probability when replacing the original…
This paper deals with a parabolic partial differential equation that includes a non-linear nonlocal in time term. This term is the product of a so-called interaction potential and the solution of the problem. The interaction potential…
The diffusion equation is a universal and standard textbook model for partial differential equations (PDEs). In this work, we revisit its solutions, seeking, in particular, self-similar profiles. This problem connects to the classical…
We present here a review of existing analytical methods to solve boundary value problems of diffusion in media containing N non-overlapping inclusions.
In this work two-point boundary value problem for one class of second order ordinary differential equations with variable coefficients is solved.