On global existence and blowup of solutions of Stochastic Keller–Segel type equation

Misiats, Oleksandr; Stanzhytskyi, Oleksandr; Topaloglu, Ihsan

doi:10.1007/s00030-021-00735-2

Cited by 6 publications

(1 citation statement)

References 22 publications

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“…Fractional nonlinear differential equations in chain solutions such as viscoelasticity, chaos and turbulence, aerospace, polymer materials, as well as non-Newtonian mechanics and other applied science fields, has a wide range of applications. The authors using the tools of nonlinear functional analysis, in order to study the existence theory and properties of solutions of several types of fractional nonlinear differential equations (groups), Misiats O et al, strive to find the conditions that make the corresponding nonlinear equation (group) solutions exist and are easier to verify or test, and the good properties of the solutions [1]; At the same time, we strive to construct an iterative approximation sequence that converges to the solution, and give an error estimation formula for the corresponding approximate solution. Fractional calculus has almost the same development history as integer calculus, it has a history of more than 300 years since it was proposed.…”

Section: Introductionmentioning

confidence: 99%

Optimal Research in Piano Shape Sound and Sound Propagation Model Based on Nonlinear Differential Equations

2022

Applied Mathematics and Nonlinear Sciences

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Nonlinear differential equations are being used in many applied science fields such as engineering, there are more and more applications, such as musical instrumentation, chemistry, aerodynamics, cybernetics, signal and image processing, biophysics, complex media dynamics, etc. Mainly based on the analysis of the vibration and attenuation characteristics of piano strings, and on the theoretical basis of the discussion on the resonance effect of the resonance system, the model of the piano music simulation system is constructed, investigated a class of fractional nonlinear differential (integrative-differential) equations and systems of equations, fractional nonlinear differential equations on unbounded domains, and with multiple different fractional derivatives, and the existence of solutions to integral nonlinear impulse differential equations, uniqueness, multiple solutions, eigenvalue interval, as well as monotonic iterative sequences and error estimates that converge to the solutions of the corresponding equations. Finally, from the pitch frequency detection, formant point frequency estimation, and three aspects of spectrogram analysis, subjective evaluation experiments are carried out on the algorithm, and the experimental results verify the effectiveness of musical simulation.

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Section: Introductionmentioning

confidence: 99%

Optimal Research in Piano Shape Sound and Sound Propagation Model Based on Nonlinear Differential Equations

2022

Applied Mathematics and Nonlinear Sciences

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Blow-up for a stochastic model of chemotaxis driven by conservative noise on $$\mathbb {R}^2$$

Mayorcas

Tomašević

2023

J. Evol. Equ.

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We establish criteria on the chemotactic sensitivity $$\chi $$ χ for the non-existence of global weak solutions (i.e., blow-up in finite time) to a stochastic Keller–Segel model with spatially inhomogeneous, conservative noise on $$\mathbb {R}^2$$ R 2 . We show that if $$\chi $$ χ is sufficiently large then blow-up occurs with probability 1. In this regime, our criterion agrees with that of a deterministic Keller–Segel model with increased viscosity. However, for $$\chi $$ χ in an intermediate regime, determined by the variance of the initial data and the spatial correlation of the noise, we show that blow-up occurs with positive probability.

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Global solutions of aggregation equations and other flows with random diffusion

Rosenzweig

Staffilani

2022

Probab. Theory Relat. Fields

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Aggregation equations, such as the parabolic-elliptic Patlak–Keller–Segel model, are known to have an optimal threshold for global existence versus finite-time blow-up. In particular, if the diffusion is absent, then all smooth solutions with finite second moment can exist only locally in time. Nevertheless, one can ask whether global existence can be restored by adding a suitable noise to the equation, so that the dynamics are now stochastic. Inspired by the work of Buckmaster et al. (Int Math Res Not IMRN 23:9370–9385, 2020) showing that, with high probability, the inviscid SQG equation with random diffusion has global classical solutions, we investigate whether suitable random diffusion can restore global existence for a large class of active scalar equations in arbitrary dimension with possibly singular velocity fields. This class includes Hamiltonian flows, such as the SQG equation and its generalizations, and gradient flows, such as those arising in aggregation models. For this class, we show global existence of solutions in Gevrey-type Fourier–Lebesgue spaces with quantifiable high probability.

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On global existence and blowup of solutions of Stochastic Keller–Segel type equation

Cited by 6 publications

References 22 publications

Optimal Research in Piano Shape Sound and Sound Propagation Model Based on Nonlinear Differential Equations

Optimal Research in Piano Shape Sound and Sound Propagation Model Based on Nonlinear Differential Equations

Blow-up for a stochastic model of chemotaxis driven by conservative noise on $$\mathbb {R}^2$$

Global solutions of aggregation equations and other flows with random diffusion

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