TY - JOUR
T1 - Well-Posedness and Regularity Analyses for Nonlocal Nonautonomous System
AU - Sun , Rui
AU - Zhang , Lijuan
AU - Deng , Weihua
JO - CSIAM Transactions on Applied Mathematics
VL - 3
SP - 593
EP - 624
PY - 2025
DA - 2025/09
SN - 6
DO - http://doi.org/10.4208/csiam-am.SO-2024-0037
UR - https://global-sci.org/intro/article_detail/csiam-am/24376.html
KW - Stochastic representation, time fractional nonautonomous equation, well-posedness, regularity
AB - <p style="text-align: justify;">The time-space nonlocal evolution equations are powerful implementation
for modeling anomalous diffusion. In this research, we study the nonlocal nonautonomous reaction-diffusion equation<br/></p><p style="text-align:center"><img src="https://admin.global-sci.org/uploads/ueditor/image/20250911/1757560177280223.png" title="1757560177280223.png" alt="image.png"/></p><p style="text-align: justify;">where $\chi$ is a Lusin space, $∂^w_t$ is a generalized time fractional derivative, $κ$ is a bounded
reaction rate, and $\mathcal{L}$ is an infinitesimal generator in terms of semigroup induced by
a symmetric Markov process $X.$ We show that the stochastic representation $u(t,x)$ defined by<br/></p><p style="text-align:center"><img src="https://admin.global-sci.org/uploads/ueditor/image/20250911/1757560192869330.png" title="1757560192869330.png" alt="image.png"/></p><p style="text-align: justify;">is the unique mild as well as weak solution. By further analysis, one can get that the
above stochastic representation is also the unique strong solution, and the higher spatial and temporal regularity are obtained. In some particular cases, the corresponding
dynamical behaviors are displayed.<br/></p>