Nonnegative solutions to time fractional Keller–Segel system

Akilandeeswari, A.; Tyagi, Jagmohan

doi:10.1002/mma.6880

Cited by 5 publications

(7 citation statements)

References 57 publications

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“…. 35 At the opposite of the (N-S) equations, the theory of time-fractional KS equations is not so rich, and many aspects of this type of equations need to be developed; for example, there are a few results in the literature about special solutions to model (1.1) (see previous studies 25,[36][37][38].…”

Section: Resultsmentioning

confidence: 99%

“…Many follow-up studies to the present one are possible. One is to establish the nonnegative solutions (see, e.g., Aruchamy and Tyagi 25 ).…”

Section: Discussionmentioning

confidence: 99%

“…The existence of weak solutions for a special case of time‐fractional compressible Navier–Stokes (N–S) equations with constant density and time‐fractional KS equations in

ℝ^{2}

is then proved as model problems. In a previous research, 25 the authors established the existence of nonnegative weak solutions to time‐fractional KS system with Dirichlet boundary condition in a bounded domain with smooth boundary. Under suitable assumptions on the initial conditions, they establish the existence of solutions to the system by using the Galerkin approximation method.…”

Section: Introductionmentioning

confidence: 99%

“…We only so mention the works in homogeneous Besov spaces

{\overset{B}{true}}_{p, \infty}^{\frac{N}{p} - 1} {false(ℝ false)}^{n}

for p > N , 27 homogeneous Fourier–Besov spaces

F {\overset{B}{true}}_{p, \infty}^{N - 1 - \frac{N}{p}}

, 28,29 homogeneous weak‐Herz spaces

W {\overset{K}{true}}_{N, \infty}^{0} false(ℝ^{N} false)

, 30 homogeneous Fourier–Herz spaces

F {\overset{B}{true}}_{1, r}^{- 1}

with r ∈ [1, 2], 28,31,32 homogeneous Besov–Morrey spaces

{scriptN}_{r, q, \infty}^{\frac{N}{r} - 1}

with r > N 33,34 and homogeneous Besov‐weak‐Herz (BWH) spaces

\overset{B}{true} W {\overset{K}{true}}_{p, q, \infty}^{β, β + \frac{N}{p} - 1}

35 . At the opposite of the (N–S) equations, the theory of time‐fractional KS equations is not so rich, and many aspects of this type of equations need to be developed; for example, there are a few results in the literature about special solutions to model () (see previous studies 25,36–38 ).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Well‐posedness and asymptotic behavior for the fractional Keller–Segel system in critical Besov–Herz‐type spaces

Azevedo

Bezerra

Cuevas

et al. 2022

Math Methods in App Sciences

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Section: Resultsmentioning

confidence: 99%

“…Many follow-up studies to the present one are possible. One is to establish the nonnegative solutions (see, e.g., Aruchamy and Tyagi 25 ).…”

Section: Discussionmentioning

confidence: 99%

“…The existence of weak solutions for a special case of time‐fractional compressible Navier–Stokes (N–S) equations with constant density and time‐fractional KS equations in

ℝ^{2}

Section: Introductionmentioning

confidence: 99%

“…We only so mention the works in homogeneous Besov spaces

{\overset{B}{true}}_{p, \infty}^{\frac{N}{p} - 1} {false(ℝ false)}^{n}

for p > N , 27 homogeneous Fourier–Besov spaces

F {\overset{B}{true}}_{p, \infty}^{N - 1 - \frac{N}{p}}

, 28,29 homogeneous weak‐Herz spaces

W {\overset{K}{true}}_{N, \infty}^{0} false(ℝ^{N} false)

, 30 homogeneous Fourier–Herz spaces

F {\overset{B}{true}}_{1, r}^{- 1}

with r ∈ [1, 2], 28,31,32 homogeneous Besov–Morrey spaces

{scriptN}_{r, q, \infty}^{\frac{N}{r} - 1}

with r > N 33,34 and homogeneous Besov‐weak‐Herz (BWH) spaces

\overset{B}{true} W {\overset{K}{true}}_{p, q, \infty}^{β, β + \frac{N}{p} - 1}

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Well‐posedness and asymptotic behavior for the fractional Keller–Segel system in critical Besov–Herz‐type spaces

Azevedo

Bezerra

Cuevas

et al. 2022

Math Methods in App Sciences

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show abstract

“…On the other hand, there is a little research (although, cf. Aruchamy and Tyagi [2]) on the systems with the Dirichlet boundary condition. Under the Neumann boundary condition, (KS) has the mass conservation law, which tells us that the amounts of the cellular slime molds do not change in time.…”

mentioning

confidence: 99%

Construction of unique mild solution and continuity of solution for the small initial data to 1-D Keller-Segel system

Yahagi¹

2022

DCDS-B

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In this paper, a one-dimensional Keller-Segel system of parabolicparabolic type which is defined on the bounded interval with the Dirichlet boundary condition is considered. Under the assumption that initial data is sufficiently small, a unique mild solution to the system is constructed and the continuity of solution for the initial data is shown, by using an argument of successive approximations.

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Well‐posedness and blow‐up of the fractional Keller–Segel model on domains

Costa

Cuevas

Silva

et al. 2023

Mathematische Nachrichten

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This work deals with well‐posedness and blow‐up in the setting of Lebesgue and Besov spaces to the time‐fractional Keller–Segel model for chemotaxis under homogeneous Neumann boundary conditions in a smooth domain of . The KS model consists in a coupled system of partial differential equations. In particular, we also treat the unique continuation of the solution and the persistence of continuous dependence on the initial data for the continued solution.

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Nonnegative solutions to time fractional Keller–Segel system

Cited by 5 publications

References 57 publications

Well‐posedness and asymptotic behavior for the fractional Keller–Segel system in critical Besov–Herz‐type spaces

Well‐posedness and asymptotic behavior for the fractional Keller–Segel system in critical Besov–Herz‐type spaces

Construction of unique mild solution and continuity of solution for the small initial data to 1-D Keller-Segel system

Well‐posedness and blow‐up of the fractional Keller–Segel model on domains

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