A simple variational approach to the estimation of timeseries is studied in detail and mathematical rigor. The functional in question is a complexity penalized sum of squares. The results include existence, uniqueness, continuous dependence on parameters, and stability, in dependence of parameters and data, of the statistical estimate.

In this paper we are concerned with a nonlocal problem of a coupled system of differential equations. We study the local existence of the solution and its continuous dependence. The global existence and its uniform stability is being studied. Mathematics subject classification (2010): 34B18, 34B10.

We consider a model for supply chains governed by partial differential equations. The mathematical properties of a continuous model are discussed and existence and uniqueness is proven. Moreover, Lipschitz continuous dependence on the initial data is proven. We make use of the front tracking method to construct approximate solutions. The obtained results extend the preliminary work of [12].

In this paper we obtain existence and (suitable) uniqueness and continuous dependence for the KP-I equation for finite time and small data in the intersection of the energy space and a natural weighted L space.

In the present paper, we investigate the existence, uniqueness and continuous dependence on initial data of mild solutions of second order nonlocal semilinear functional integrodifferential equations of more general type with delay in Banach spaces. Our analysis is based on the theory of strongly continuous cosine family of operators and modified version of Banach contraction theorem.

We prove short time existence, uniqueness and continuous dependence on the initial data of smooth solutions of quasilinear locally parabolic equations of arbitrary even order on closed manifolds. CONTENTS

We present existence, uniqueness and continuous dependence (with respect to probability distributions on polarization parameters) of solutions in Maxwell systems. This provides a theoretical and computational foundation for associated inverse problems.