相关论文: Well-posedness of general 1D Initial Boundary Valu…

We consider the initial boundary value problem (IBVP) for a non-local scalar conservation laws in one space dimension. The non-local operator in the flux function is not a mere convolution product, but it is assumed to be aware of…

A Lax-Oleinik type explicit formula for 1D scalar balance laws has been recently obtained for the pure initial value problem by Adimurthi et al. in [1]. In this article, by introducing a suitable boundary functional, we establish a…

We prove the stability with respect to the flux of solutions to initial-boundary value problems for scalar non-autonomous conservation laws in one space dimension. Key estimates are obtained through a careful construction of the solutions.

We consider four definitions of solution to the initial-boundary value problem for a scalar balance laws in several space dimensions. These definitions are generalised to the same most general framework and then compared. The first aim of…

We consider well-balanced schemes for the following 1D scalar conservation law with source term: d_t u + d_x f(u) + z'(x) b(u) = 0. More precisely, we are interested in the numerical approximation of the initial boundary value problem for…

Initial-boundary value problems in a bounded rectangle with different types of boundary conditions for two-dimensional Zakharov-Kuznetsov equation are considered. Results on global well-posedness in the classes of weak and regular solution…

The initial boundary value problem for a class of scalar non autonomous conservation laws in one space dimension is proved to be well posed and stable with respect to variations in the flux. Targeting applications to traffic, the regularity…

A well-posed initial-boundary value problem is formulated for the model problem of the vector wave equation subject to the divergence-free constraint. Existence, uniqueness and stability of the solution is proved by reduction to a system…

The initial-boundary value problem for a general balance law in a bounded domain is proved to be well posed. Indeed, we show the existence of an entropy solution, its uniqueness and its Lipschitz continuity as a function of time, of the…

The paper considers the system of pressureless gas dynamics in one space dimension. The question of solvability of the initial-boundary value problem is addressed. Using the method of generalized potentials and characteristic triangles,…

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…

We study the well-posedness for initial boundary value problems associated with time fractional diffusion equations with non-homogenous boundary and initial values. We consider both weak and strong solutions for the problems. For weak…

This article deals with the initial-boundary value problem for a moderately coupled system of time-fractional diffusion equations. Defining the mild solution, we establish fundamental unique existence, limited smoothing property and…

We derive well-posed boundary conditions for the linearized Serre equations in one spatial dimension by utilizing the energy method. An energy stable and conservative discontinuous Galerkin spectral element method with simple upwind…

We consider conservation laws with source terms in a bounded domain with Dirichlet boundary conditions. We first prove the existence of a strong trace at the boundary in order to provide a simple formulation of the entropy boundary…

An initial-boundary value problem for a time-fractional subdiffusion equation with an arbitrary order elliptic differential operator is considered. Uniqueness and existence of the classical solution of the posed problem are proved by the…

This paper is concerned with the initial-boundary value problem for the Einstein equations in a first-order generalized harmonic formulation. We impose boundary conditions that preserve the constraints and control the incoming gravitational…

We examine initial-boundary value problems for diffusion equations with distributed order time-fractional derivatives. We prove existence and uniqueness results for the weak solution to these systems, together with its continuous dependency…

We discuss initial-boundary value problems of arbitrary spatial order subject to arbitrary boundary conditions. We formalise the concept of the conditioning of such a problem and show that it represents a necessary criterion for…

Consider the general scalar balance law $\partial_t u + \Div f(t, x,u) = F(t,x,u)$ in several space dimensions. The aim of this note is to estimate the dependence of its solutions from the flow $f$ and from the source $F$. To this aim, a…