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| Existence and Blowup of Solutions for Neutral Partial Integro-differential Equations with State-dependent Delay |
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| KeyWord:Neutral partial integro-differential equation Analytic semigroup Resolvent operator Fractional power operator State-dependent delay |
| Author Name | Affiliation | | Jianbo Zhu | School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, East
China Normal University, Shanghai 200241, China | | Xingxing Wang | School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, East
China Normal University, Shanghai 200241, China | | Xianlong Fu | School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, East
China Normal University, Shanghai 200241, China |
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| 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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