Publication Cover
Applicable Analysis
An International Journal
Volume 40, 1991 - Issue 2-3
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Original Articles

On B-evolution theory and dynamic boundary conditions on a portion of the boundary

Pages 151-172 | Received 16 Feb 1990, Published online: 10 May 2007
 

Abstract

In this paper we treat an elliptic boundary value problem of mixed type in which the boundary conditions on one of two disjoint boundaries are of a dynamic nature. The coefficients of the differential operators involved are dependent on the spatial as well as the time variable. We follow the approach of an abstract evolution problem of the form d(Bu(t))⊟/dt = A(t)u(t), Bu(0) = y in which A and B are unbounded, not necessarily closed operators, from a Banach space X to a Banach space Y, whose common domain is time-dependent. By treating the abstract problem with the aid of the theory of B-evolutions, it is shown that the boundary value problem is well-posed for arbitrary initial states in Y

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