Global existence in a fully parabolic attraction-repulsion chemotaxis system with singular sensitivities and proliferation

Jiao, Zhan; Jadlovská, Irena; Li, Tongxing

doi:10.1016/j.jde.2024.07.005

Journal of Differential Equations

2024

DOI: 10.1016/j.jde.2024.07.005

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Global existence in a fully parabolic attraction-repulsion chemotaxis system with singular sensitivities and proliferation

Zhan Jiao,

Irena Jadlovská,

Tongxing Li

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2024

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Cited by 3 publications

References 43 publications

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On coupled non-linear Schrödinger systems with singular source term

Almuthaybiri,

Saanouni

2024

MATH

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This work studies a coupled non-linear Schrödinger system with a singular source term. First, we investigate the question of the local existence of solutions. Second, one proves the existence of global solutions which scatter in some Sobolev spaces. Finally, one establishes the existence of non-global solutions. The main difficulty here is to overcome the regularity problem in the non-linearity. Indeed, because of the singularity of the source term, the classical contraction method in the energy space fails in such a regime. So, this paper is to fill such a gap in the literature. The argument follows ideas in T. Cazenave and I. Naumkin (<italic>Comm. Contemp. Math.</italic>, <bold>19</bold> (2017), 1650038). This consists to remark that the singularity problem is only near the origin. So, one needs to impose that the solution stays away from zero. This is not trivial, since there is no maximum principle for the Schrödinger equation. The existence of global solutions which scatter follows with the pseudo-conformal transformation via the existence of local solutions. Finally, the existence of non-global solutions follows with the classical variance method.

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On coupled non-linear Schrödinger systems with singular source term

Almuthaybiri,

Saanouni

2024

MATH

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Improved Kneser-type oscillation criterion for half-linear dynamic equations on time scales

Hassan,

Menaem,

Zaidi

et al. 2024

MATH

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We study the Kneser-type oscillation criterion for a class of second-order half-linear functional dynamic equations on an arbitrary time scale utilizing the integral averaging approach and the Riccati transformation method. The results show an improvement in Kneser-type when compared to some known results. We provide some illustrative examples to demonstrate the significance of our main results.

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Artificial neural networks for stability analysis and simulation of delayed rabies spread models

Shafqat,

Alsaadi

2024

MATH

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Rabies remains a significant public health challenge, particularly in areas with substantial dog populations, necessitating a deeper understanding of its transmission dynamics for effective control strategies. This study addressed the complexity of rabies spread by integrating two critical delay effects—vaccination efficacy and incubation duration—into a delay differential equations model, capturing more realistic infection patterns between dogs and humans. To explore the multifaceted drivers of transmission, we applied a novel framework using piecewise derivatives that incorporated singular and non-singular kernels, allowing for nuanced insights into crossover dynamics. The existence and uniqueness of solutions was demonstrated using fixed-point theory within the context of piecewise derivatives and integrals. We employed a piecewise numerical scheme grounded in Newton interpolation polynomials to approximate solutions tailored to handle singular and non-singular kernels. Additionally, we leveraged artificial neural networks to split the dataset into training, testing, and validation sets, conducting an in-depth analysis across these subsets. This approach aimed to expand our understanding of rabies transmission, illustrating the potential of advanced mathematical tools and machine learning in epidemiological modeling.

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Global existence in a fully parabolic attraction-repulsion chemotaxis system with singular sensitivities and proliferation

Cited by 3 publications

References 43 publications

On coupled non-linear Schrödinger systems with singular source term

On coupled non-linear Schrödinger systems with singular source term

Improved Kneser-type oscillation criterion for half-linear dynamic equations on time scales

Artificial neural networks for stability analysis and simulation of delayed rabies spread models

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