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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…
In this paper, we propose a review of the free boundary formulation for BVPs defined on semi-infinite intervals. The main idea and theorem are illustrated, for the reader convenience, by using a class of second-order BVPs. Moreover, we are…
We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary…
In this paper we introduce some new concepts for second-order hyperbolic equations: two-point boundary value problem, global exact controllability and exact controllability. For several kinds of important linear and nonlinear wave equations…
We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…
We consider a wide class of linear boundary-value problems for systems of $r$-th order ordinary differential equations whose solutions range over the normed complex space $(C^{(n)})^m$ of $n\geq r$ times continuously differentiable…
In this paper we analyse full discretizations of an initial boundary value problem (IBVP) related to reaction-diffusion equations. To avoid possible order reduction, the IBVP is first transformed into an IBVP with homogeneous boundary…
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 study initial value problem for a system consisting of an integer order and distributed-order fractional differential equation describing forced oscillations of a body attached to a free end of a light viscoelastic rod. Explicit form of…
Using the direct method of the calculus of variations we investigate the existence, uniqueness and continuous dependence on parameters for solutions of second order discrete anisotropic equations with Dirichlet boundary conditions.
Under consideration are mathematical models of heat and mass transfer. We study inverse problems of recovering lower-order coefficients in a second order parabolic equation. The coefficients are representable in the form of a finite…
In this work we prove that the initial value problem (IVP) associated to the fractional two-dimensional Benjamin-Ono equation $$\left. \begin{array}{rl} u_t+D_x^{\alpha} u_x +\mathcal Hu_{yy} +uu_x &=0,\qquad\qquad (x,y)\in\mathbb R^2,\;…
We study linear boundary-value problems for systems of first-order ordinary differential equations with the most general boundary conditions in the normed spaces of continuously differentiable functions on a finite closed interval. The…
We study the large time behaviour of the solution of a linear dispersive PDEs posed on a finite interval, when the prescribed boundary conditions are time periodic. We use the approach pioneered in Fokas & Lenells 2012 for nonlinear…
We present a new approach to compute selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. Our method requires computing generalized eigenvalue problems of the same size as the matrices of the initial two-parameter…
In the article, in a rectangular domain, by the Fourier method, the initial boundary value problem for a high-order equation with two lines of degeneracy with a fractional derivative in the sense of Caputo is investigated for uniqueness and…
We discuss several classes of linear second order initial-boundary value problems, where damping terms appear in the main wave equation as well as in the dynamic boundary condition. We investigate their well-posedness and describe some…
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…
In [2] we introduced a method combining together an observability inequality and a spectral decomposition to get a logarithmic stability estimate for the inverse problem of determining both the potential and the damping coefficient in a…
We focus on the initial boundary value problem for a general scalar balance law in one space dimension. Under rather general assumptions on the flux and source functions, we prove the well-posedness of this problem and the stability of its…