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

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Abstract | References | Similar Articles | Additional Information

Abstract: The abstract semilinear Volterra integrodifferential equation

*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.

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DOI:
https://doi.org/10.1090/S0002-9939-1978-0467214-4

Keywords:
Abstract Volterra integrodifferential equation,
semigroup of bounded linear operators,
infinitesimal generator,
existence,
uniqueness,
asymptotic behavior

Article copyright:
© Copyright 1978
American Mathematical Society