Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

An abstract semilinear Volterra integrodifferential equation


Author: G. F. Webb
Journal: Proc. Amer. Math. Soc. 69 (1978), 255-260
MSC: Primary 45K05
MathSciNet review: 0467214
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The abstract semilinear Volterra integrodifferential equation

$\displaystyle u'(t) = Au(t) + \int_0^t {g(t - s,u(s))ds + f(t),\quad t \geqslant 0,u(0) = x \in X,} $

is investigated, where A is the infinitesimal generator of a semigroup of linear operators in a Banach space X and g is nonlinear and unbounded in its second place. Some results are proved concerning local existence, global existence, continuous dependence upon initial values, and asymptotic stability. The method used treats the equation in the domain of A with the graph norm employing results from linear semigroup theory concerning abstract inhomogeneous linear differential equations.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 45K05

Retrieve articles in all journals with MSC: 45K05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0467214-4
PII: S 0002-9939(1978)0467214-4
Keywords: Abstract Volterra integrodifferential equation, semigroup of bounded linear operators, infinitesimal generator, existence, uniqueness, asymptotic behavior
Article copyright: © Copyright 1978 American Mathematical Society