Existence, Uniqueness and Stability of Strictly Positive Entire Solutions to a Fractional Keller‐Segel Model With Time‐Space Dependent Logistic Source

ABSTRACT This paper is devoted to the study of the asymptotic dynamics in the fractional parabolic‐elliptic Keller‐Segel system on with time‐space dependent logistic source. In [36], among others, we established a theory on the global existence, uniqueness, pointwise and uniform persistence of classical solutions to this fractional Keller‐Segel system. In this paper, we prove the existence, uniqueness, and stability of strictly positive entire solutions of this system. In summary, the results of our paper extend some of the results obtained earlier in [36].