Approximation of a bounded solution of a linear difference equation on Z2 by solutions of corresponding boundary-value problems in a Banach space

1995 ◽  
Vol 47 (4) ◽  
pp. 622-628
Author(s):  
M. F. Gorodnii
Keyword(s):  
Banach Space ◽  
Difference Equation ◽  
Boundary Value Problems ◽  
Bounded Solution ◽  
Boundary Value ◽  
Linear Difference Equation

On the convolution operators arising in the study of abstract initial boundary value problems

1996 ◽  
Vol 126 (3) ◽  
pp. 515-539 ◽  
Author(s):  
I. Alonso-Mallo ◽  
C. Palencia
Keyword(s):  
Banach Space ◽  
Boundary Value Problems ◽  
Infinitesimal Generator ◽  
Boundary Value ◽  
Continuous Mapping ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Convolution Operators ◽  
Image Position ◽  
Initial Boundary Value

We consider convolution operators arising in the study of abstract initial boundary value problems. These operators are of the formwhere {S(t)}t ≧0 is a C0-semigroup in a Banach space X,, with infinitesimal generator A0,: D(A0), ⊂ X, → X, and K(z): Y → X is a linxear, continuous mapping defined in another Banach space Y., We study the continuity of T between the spaces Lp([0, + ∞), Y), and Lq([0, + ∞), X), 1 ≦ p, q, ≦ + ∞. We give several examples of the applicability of the results to some familiar initial boundary value problems, including both parabolic and hyperbolic cases.

Sign in / Sign up

Export Citation Format

Share Document