A method of lines for a nonlinear abstract functional evolution equation

Authors:
A. G. Kartsatos and M. E. Parrott

Journal:
Trans. Amer. Math. Soc. **286** (1984), 73-89

MSC:
Primary 34K30

MathSciNet review:
756032

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Abstract: Let be a real Banach space with uniformly convex. A method of lines is introduced and developed for the abstract functional problem (E)

The operators are -accretive and is a global Lipschitzian-like function in its two variables. Further conditions are given for the convergence of the method to a strong solution of (E). Recent results for perturbed abstract ordinary equations are substantially improved. The method applies also to large classes of functional parabolic problems as well as problems of integral perturbations. The method is straightforward because it avoids the introduction of the operators and the corresponding use of nonlinear evolution operator theory.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1984-0756032-2

Keywords:
Functional evolution equation,
uniformly convex dual,
method of lines,
-accretive operator

Article copyright:
© Copyright 1984
American Mathematical Society