TY - JOUR
T1 - Existence and Blowup of Solutions for Neutral Partial Integro-Differential Equations with State-Dependent Delay
AU - Zhu , Jianbo
AU - Wang , Xingxing
AU - Fu , Xianlong
JO - Journal of Nonlinear Modeling and Analysis
VL - 2
SP - 287
EP - 313
PY - 2021
DA - 2021/04
SN - 2
DO - http://doi.org/10.12150/jnma.2020.287
UR - https://global-sci.org/intro/article_detail/jnma/18812.html
KW - Neutral partial integro-differential equation, Analytic semigroup,
Resolvent operator, Fractional power operator, State-dependent delay.
AB - <p style="text-align: justify;">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.</p>