Related papers: Wellposedness of the initial boundary value proble…
In this paper we consider an initial boundary value problem for a semilinear parabolic equation with nonlinear nonlocal boundary condition. We prove comparison principle, the existence theorem of a local solution and study the problem of…
We study the mathematical properties of time-dependent flows of incompressible fluids that respond as an Euler fluid until the modulus of the symmetric part of the velocity gradient exceeds a certain, a-priori given but arbitrarily large,…
This paper investigates the initial value problem for a system of one-dimensional fourth-order dispersive partial differential-integral equations with nonlinearity involving derivatives up to second order. Examples of the system arise in…
It is well known that the tropical climate model is an important model to describe the interaction of large scale flow fields and precipitation in the tropical atmosphere. In this paper, we address the issue of global well-posedness for 2D…
This paper focuses on the two-dimensional Benjamin-Bona-Mahony and Benjamin-Bona-Mahony-Burgers equations with a general flux function. The aim is at the global (in time) well-posedness of the initial-and boundary-value problem for these…
An initial-boundary value problem with homogeneous Dirichlet boundary conditions for three-dimensional Zakharov-Kuznetsov equation is considered. Results on global existence, uniqueness and large-time decay of weak solutions in certain…
We consider initial boundary value problems with the homogeneous Neumann boundary condition. Given an initial value, we establish the uniqueness in determining a spatially varying coefficient of zeroth-order term by a single measurement of…
We study the initial value problem for Lovelock and Horndeski theories of gravity. We show that the equations of motion of these theories can be written in a form that, at weak coupling, is strongly hyperbolic and therefore admits a…
We discuss the initial-boundary value problem for the Baumgarte-Shapiro-Shibata-Nakamura evolution system of Einstein's field equations which has been used extensively in numerical simulations of binary black holes and neutron stars. We…
We consider the linear wave equation $V(x) u_{tt}(x, t) - u_{xx}(x, t) = 0$ on $[0, \infty)\times[0, \infty)$ with initial conditions and a nonlinear Neumann boundary condition $u_x(0, t) = (f(u_t(0,t)))_t$ at $x=0$. This problem is an…
In this paper, we are concerned with the initial-boundary value problem to the 2D magneto-micropolar system with zero angular viscosity in a smooth bounded domain. We prove that there exists a unique global strong solution of such a system…
This article uses the conformal Einstein equations and the conformal representation of spatial infinity introduced by Friedrich to analyse the behaviour of the gravitational field near null and spatial infinity for the development of…
The question of boundary conditions in conformal field theories is discussed, in the light of recent progress. Two kinds of boundary conditions are examined, along open boundaries of the system, or along closed curves or ``seams''. Solving…
This paper is concerned with the Dirichlet initial-boundary value problem of a 2-D parabolic-elliptic system proposed to model the formation of biological transport networks. Even if global weak solutions for this system are known to exist,…
We prove the first positive results concerning boundary value problems in the upper half-space of second order parabolic systems only assuming measurability and some transversal regularity in the coefficients of the elliptic part. To do so,…
We address nonautonomous initial boundary value problems for decoupled linear first-order one-dimensional hyperbolic systems, investigating the phenomenon of finite time stabilization. We establish sufficient and necessary conditions…
We develop a general method of proving the ellipticity of boundary value problems for the stationary vacuum space time, by showing that the stationary vacuum field equations are elliptic subjected to a geometrically natural collection of…
We prove the well--posedness of a dynamical perfect plasticity model under general assumptions on the stress constraint set and on the reference configuration. The problem is studied by combining both calculus of variations and hyperbolic…
When a (frequency-domain) boundary value problem involving a homogeneous linear material is solved to assess the validity of the Post constraint, a conflict arises between the fundamental differential equations of electromagnetism in the…
In this work we prove that the initial-boundary value problem (IBVP) for the fifth order Korteweg-de Vries equation \begin{align*} \left. \begin{array}{rlr} u_t+\partial_x^5 u+u\partial_x u&\hspace{-2mm}=0,&\quad x\in\mathbb R^+,\;…