This note is devoted to study an inverse Cauchy problem in a Hilbert space H for fractional abstract differential equations of the form; ), ( ) ( ) ( = ) ( t g t f t u A dt t u d    with the initial condition H u u = (0) 0 and the overdetermination condition: ), ( = ) ), ( ( t w v t u where (.,.) is the inner product in H , f is a real unknown function w is a given real function, 0 u , v ar...

This paper is concerned with characterizations of those linear, closed, but not necessarily densely defined operators A on a Banach space E with nonempty resolvent set for which the abstract Cauchy problem u'(t) = Au(t), u(0) = x has unique, exponentially bounded solutions for every initial value x e D(A). Investigating these operators we are led to the class of "integrated semigroups". Among o...

We consider the problem to find moment functions of solution Cauchy for a first-order linear inhomogeneous differential equation with random coefficients in Banach space. The is reduced initial nonrandom ordinary and variational derivatives. obtain explicit expressions mathematical expectation second-order mixed equation.

The Cauchy problem is studied for a perturbed wave equation in half-plane with data given on part of the space-time boundary. consideration describes process laterally inhomogeneous medium. A reconstruction algorithm proposed, which applicable to determining nonstationary field from boundary arising geophysics.

The article investigates the inverse problem for a complete, inhomogeneous, higher-order Sobolev type equation, together with Cauchy and overdetermination conditions. This was reduced to two equivalent problems in aggregate: regular singular. For these problems, theory of polynomially bounded operator pencils is used. unknown coefficient original equation restored using method successive approx...

Abstract. We consider the Cauchy problem for an elliptic operator, formulated as a Nash game. The over specified Cauchy data are split among two players : the first player solves the elliptic equation with the Dirichlet part of the Cauchy data prescribed over the accessible boundary, and a variable Neumann condition (which we call first player’s strategy) prescribed over the inaccessible part o...

We consider the Cauchy problem for a first-order linear inhomogeneous system of partial differential equations with random processes as coefficients. Explicit formulas mathematical expectation solution are obtained. Examples systems Gaussian and uniformly distributed coefficients considered. An example calculations simplified learning model at microlevel is given.