Related papers: Conditional stability for backward parabolic equat…

We prove logarithmic conditional stability up to the final time for backward-parabolic operators whose coefficients are Log-Lipschitz continuous in $t$ and Lipschitz continuous in $x$. The result complements previous achievements of Del…

In this paper we present an improvement of [Math. Ann. 345 (2009), 213--243], where the authors proved a result concerning continuous dependence for backward parabolic operators whose coefficients are Log-Lipschitz in $t$ and $C^2$ in $x$.…

We prove continuous dependence on initial data for a backward parabolic operator whose leading coefficients are Osgodd continuous in time. This result fills the gap between uniqueness and continuity results obtained so far.

This work deals with Lipschitz stability for a parametric version of the general second order Ordinary Differential Equation (ODE) initial-value Cauchy problem. We first establish a Lipschitz stability result for this problem under a…

We establish a general existence and uniqueness result of $L^1$ solution for a multidimensional backward stochastic differential equation (BSDE for short) with generator $g$ satisfying a one-sided Osgood condition as well as a general…

We consider a parabolic equation whose coefficients are Log-Lipschitz continuous in $t$ and Lipschitz continuous in $x$. Combining a recent conditional stability result with a well posed variational problem, we reconstruct the initial…

In this work we determine the second-order coefficient in a parabolic equation from the knowledge of a single final data. Under assumptions on the concentration of eigenvalues of the associated elliptic operator, and the initial state, we…

We investigate the relation between the backward uniqueness and the regularity of the coefficients for a parabolic operator. A necessary and sufficient condition for uniqueness is given in terms of the modulus of continuity of the…

This work studies stability and robustness of a nonlinear system given as an interconnection of an ODE and a parabolic PDE subjected to external disturbances entering through the boundary conditions of the parabolic equation. To this end we…

For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…

We prove that solutions to Cauchy problems related to the $p$-parabolic equations are stable with respect to the nonlinearity exponent $p$. More specifically, solutions with a fixed initial trace converge in an $L^q$-space to a solution of…

We prove the backward uniqueness for general parabolic operators of second order in the whole space under assumptions that the leading coefficients of the operator are Lipschitz and their gradients satisfy certain decay conditions. This…

This paper deals with the stability of linear periodic difference delay systems, where the value at time $t$ of a solution is a linear combination with periodic coefficients of its values at finitely many delayed instants…

We prove stability for a formally determined inverse problem for a hyperbolic PDE where the coefficients depend on space and time variables. The hyperbolic operator has constant wave speed and we study the recovery of zeroth order and first…

We provide explicit conditions for uniform stability, global asymptotic stability and uniform exponential stability for dynamic equations with a single delay and a nonnegative coefficient. Some examples on nonstandard time scales are also…

In this paper, we present a framework for Stability Analysis of Systems of Coupled Linear Partial-Differential Equations. The class of PDE systems considered in this paper includes parabolic, elliptic and hyperbolic systems with Dirichelet,…

A nonlinear stochastic differential equation with the order of nonlinearity higher than one, with several discrete and distributed delays and time varying coefficients is considered. It is shown that the sufficient conditions for…

Nonlinear partial differential equations are central to physics, engineering, and finance. Except in a limited number of integrable cases, their solution generally requires numerical methods whose cost becomes prohibitive in…

We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known…

By imposing an additional integrability condition on the first component of the solution, this paper establishes an existence and uniqueness result for $L^1$ solutions of multidimensional backward stochastic differential equations (BSDEs)…