In this paper,the Cauchy problem of the classical Keller-Segel chemotaxis model with initial data of large mass is considered.By the Green’s function method and scaling technique,we prove that if‖u0‖■‖u0‖■ and...In this paper,the Cauchy problem of the classical Keller-Segel chemotaxis model with initial data of large mass is considered.By the Green’s function method and scaling technique,we prove that if‖u0‖■‖u0‖■ and κ‖Δv0‖Lp are less than some constant,then the problem always admits a unique global classical solution,even when the initial mass‖u0‖L1 is large.Moreover,the decay rates of the classical solution are also obtained.展开更多
In this paper, we consider the Neumann initial-boundary value problem for the Keller-Segel chemotaxis system with singular sensitivity <img src="Edit_4b941130-fc1e-4c9b-9626-4fd5a1f03836.bmp" alt="&q...In this paper, we consider the Neumann initial-boundary value problem for the Keller-Segel chemotaxis system with singular sensitivity <img src="Edit_4b941130-fc1e-4c9b-9626-4fd5a1f03836.bmp" alt="" />(0.1)<br /> <p> is considered in a bounded domain with smooth boundary, Ω ⊂R<sup><i>n</i></sup> (<i>n</i> ≥ 1), where <i>d</i><sub>1</sub> > 0, <i>d</i><sub>2</sub> > 0 with parameter <i>χ</i> ∈ R. When <i>d</i><sub>1</sub> = <i>d</i><sub>2</sub> + <i>χ</i>, satisfying for all initial data 0 ≤ <i>n</i><sub>0</sub> ∈ <i>C</i><sup>0</sup><img src="Edit_4898c7a9-f047-4856-b9ad-8d42ecf262a2.bmp" alt="" /> and 0 < <i>v</i><sub>0</sub>∈ <i>W</i><sup>1,∞</sup> (Ω), we prove that the problem possesses a unique global classical solution which is uniformly bounded in Ω × (0, ∞). </p>展开更多
We consider the global existence and decay of integral solutions to the parabolic-parabolic Keller-Segel system in d-dimension.On the one hand,by Banach fixed point theorem and some properties of heat kernel,we prove ...We consider the global existence and decay of integral solutions to the parabolic-parabolic Keller-Segel system in d-dimension.On the one hand,by Banach fixed point theorem and some properties of heat kernel,we prove the local existence and the global existence of integral solutions for the different initial data under some conditions that involve the size of the initial data.On the other hand,in the case of global solutions,we obtain their optimal time decay by Gronwall’s lemma.展开更多
This work is concerned with the time-fractional doubly parabolic Keller-Segel system in R^(N)(N≥1),and we derive some refined results on the large time behavior of solutions which are presupposed to enjoy some unifor...This work is concerned with the time-fractional doubly parabolic Keller-Segel system in R^(N)(N≥1),and we derive some refined results on the large time behavior of solutions which are presupposed to enjoy some uniform boundedness properties.Moreover,the well-posedness and the asymptotic stability of solutions in Marcinkiewicz spaces are studied.The results are achieved by means of an appropriate estimation of the system nonlinearity in the course of an analysis based on Duhamel-type representation formulae and the Kato-Fujita framework which consists in constructing a fixed-point argument by using a suitable time-dependent space.展开更多
基金Supported by the Natural Science Foundation of Jiangsu Province(BK20160856)the National Natural Science Foundation of China(11801137)。
文摘In this paper,the Cauchy problem of the classical Keller-Segel chemotaxis model with initial data of large mass is considered.By the Green’s function method and scaling technique,we prove that if‖u0‖■‖u0‖■ and κ‖Δv0‖Lp are less than some constant,then the problem always admits a unique global classical solution,even when the initial mass‖u0‖L1 is large.Moreover,the decay rates of the classical solution are also obtained.
文摘In this paper, we consider the Neumann initial-boundary value problem for the Keller-Segel chemotaxis system with singular sensitivity <img src="Edit_4b941130-fc1e-4c9b-9626-4fd5a1f03836.bmp" alt="" />(0.1)<br /> <p> is considered in a bounded domain with smooth boundary, Ω ⊂R<sup><i>n</i></sup> (<i>n</i> ≥ 1), where <i>d</i><sub>1</sub> > 0, <i>d</i><sub>2</sub> > 0 with parameter <i>χ</i> ∈ R. When <i>d</i><sub>1</sub> = <i>d</i><sub>2</sub> + <i>χ</i>, satisfying for all initial data 0 ≤ <i>n</i><sub>0</sub> ∈ <i>C</i><sup>0</sup><img src="Edit_4898c7a9-f047-4856-b9ad-8d42ecf262a2.bmp" alt="" /> and 0 < <i>v</i><sub>0</sub>∈ <i>W</i><sup>1,∞</sup> (Ω), we prove that the problem possesses a unique global classical solution which is uniformly bounded in Ω × (0, ∞). </p>
文摘We consider the global existence and decay of integral solutions to the parabolic-parabolic Keller-Segel system in d-dimension.On the one hand,by Banach fixed point theorem and some properties of heat kernel,we prove the local existence and the global existence of integral solutions for the different initial data under some conditions that involve the size of the initial data.On the other hand,in the case of global solutions,we obtain their optimal time decay by Gronwall’s lemma.
基金supported by the National Research and Development Agency of Chile(ANID)-Chile under Fondecyt(Grant No.1181084)。
文摘This work is concerned with the time-fractional doubly parabolic Keller-Segel system in R^(N)(N≥1),and we derive some refined results on the large time behavior of solutions which are presupposed to enjoy some uniform boundedness properties.Moreover,the well-posedness and the asymptotic stability of solutions in Marcinkiewicz spaces are studied.The results are achieved by means of an appropriate estimation of the system nonlinearity in the course of an analysis based on Duhamel-type representation formulae and the Kato-Fujita framework which consists in constructing a fixed-point argument by using a suitable time-dependent space.
