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On the Convergence of the Method of Lines for Quasi–Nonlinear Functional Evolutions in Banach Spaces
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B. J. Jin
Published/Copyright:
June 4, 2010
Abstract
This paper is concerned with the existence of global limit solutions for the quasi–nonlinear functional evolution problem
where A(t, ψ1) and G(t, ψ1, Ltψ2) are defined, with respect to ψ1, on a subspace of the space PC([–r, 0], X) of all piecewise continuous functions ƒ : [–r, 0] → X. An appropriate subspace of PC([–r, t], X) is the domain of definition of the nonlinear operators Lt, t ∈ [0, T]. The operators A(t, ψ)x are w-dissipative and Lipschitz — like in (t, ψ) which are more general conditions than those of Karsatos–Liu. The operators G and Lt are Lipschitzian mappings on their respective domains. Moreover, we investigate the uniqueness and strong solution for such problem.
Key words and phrases.: Quasi–nonlinear functional evolution equation; global limit solutions; strong solution; piecewise continuous function; w-dissipative operator; m-dissipative operator; method of line
Received: 1998-07-21
Published Online: 2010-06-04
Published in Print: 2000-June
© Heldermann Verlag
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Articles in the same Issue
- Feynman's Path Integrals and Henstock's Non-Absolute Integration
- Universally Polygonally Approximable Functions
- Differential Calculus for Complex-Valued Multifunctions
- On Analogues of Some Classical Subsets of the Real Line
- Oscillation Criteria of Comparison Type for Second Order Difference Equations
- On the Convergence of the Method of Lines for Quasi–Nonlinear Functional Evolutions in Banach Spaces
- Bounded Solutions for Nonlinear Elliptic Equations in Unbounded Domains
- A Characterization of Strict Local Minimizers of Order One for Static Minmax Problems in the Parametric Constraint Case
- On Linear Dependence of Iterates
