Global strong solution to the semi-linear Keller-Segel system of parabolic-parabolic type with small data in scale invariant spaces
By H. Kozono, Yoshie Sugiyama. 2009
56 citations recorded by the source corpus.
Abstract We shall show existence of global strong solution to the semi-linear Keller–Segel system in R n , n ⩾ 3 , of parabolic–parabolic type with small initial data u 0 ∈ H n r − 2 , r ( R n ) and v 0 ∈ H n r , r ( R n ) for max { 1 , n / 4 } r n / 2 . Our method is based on the perturbation of linealization together with the L p – L q estimates of the heat semigroup and the fractional powers of the Laplace operator. As a by-product of our method, we shall prove the decay property of solutions as the time goes to infinity.
Subfields: Cancer Research, Modeling and Simulation, Oncology
View Paper: https://www.semanticscholar.org/paper/9c6330a1871c8e5ddacdda0f51c13e7595482fdc
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In Cancer Research
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Citations in the corpus
- Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system (2011, unknown): “[32], [22], [23], [24], [9], [4], [19], [33] and also the survey [16]).”
- Small data in an optimal Banach space for the parabolic-parabolic and parabolic-elliptic Keller--Segel equations in the whole space (2013, methodology): “This explains the important litterature on Keller-Segel equations with data in scale invariant spaces such as Ld/2 [5], Ld/2,∗ [10, 12], Ḣd/p−2,p [11], Ḃ −2+d/p p,∞ [8], PM1 [3].”