Existence and Blowup of Solutions for Neutral Partial Integro-Differential Equations with State-Dependent Delay
Year: 2020
Author: Jianbo Zhu, Xingxing Wang, Xianlong Fu
Journal of Nonlinear Modeling and Analysis, Vol. 2 (2020), Iss. 2 : pp. 287–313
Abstract
In this paper, we study the existence and blowup of solutions for a neutral partial functional integro-differential equation with state-dependent delay in Banach space. The mild solutions are obtained by Sadovskii fixed point theorem under compactness condition for the resolvent operator, the theory of fractional power and $α$-norm are also used in the discussion since the nonlinear terms of the system involve spacial derivatives. The strong solutions are obtained under the lipschitz condition. In addition, based on the local existence result and a piecewise extended method, we achieve a blowup alternative result as well for the considered equation. Finally, an example is provided to illustrate the application of the obtained results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2020.287
Journal of Nonlinear Modeling and Analysis, Vol. 2 (2020), Iss. 2 : pp. 287–313
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Neutral partial integro-differential equation Analytic semigroup Resolvent operator Fractional power operator State-dependent delay.