Asymptotic behavior of a solution to the drift-diffusion equation for a fast-diffusion case

DOI10.1016/j.jde.2021.10.032zbMath1479.35540OpenAlexW3214614929MaRDI QIDQ2051739

Takayoshi Ogawa, Takeshi Suguro

Publication date: 25 November 2021

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2021.10.032

zbMATH Keywords

asymptotic behavior of solutionsfast diffusiondrift-diffusion equationRényi entropyBarenblatt self-similar solutionsnonlocal transport term

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Degenerate parabolic equations (35K65) Self-similar solutions to PDEs (35C06)

Related Items (1)

Maximal regularity and a singular limit problem for the Patlak-Keller-Segel system in the scaling critical space involving \textit{BMO}

Cites Work

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• A Mathematical Theory of Communication
• Nonlinear diffusions: extremal properties of Barenblatt profiles, best matching and delays
• Dynamic and steady states for multi-dimensional Keller-Segel model with diffusion exponent \(m > 0\)
• Extinction, decay and blow-up for Keller-Segel systems of fast diffusion type
• Asymptotic stability of a decaying solution to the Keller-Segel system of degenerate type.
• Critical mass for a Patlak-Keller-Segel model with degenerate diffusion in higher dimensions
• Best constant in Sobolev inequality
• Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions.
• Long time behavior of solutions of Nernst-Planck and Debye-Hückel drift-diffusion systems
• Stability and instability of solutions to the drift-diffusion system
• Interpolation inequalities, nonlinear flows, boundary terms, optimality and linearization
• Ground states in the diffusion-dominated regime
• Shannon's inequality for the Rényi entropy and an application to the uncertainty principle
• Improved interpolation inequalities, relative entropy and fast diffusion equations
• THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
• Entropy Methods for Diffusive Partial Differential Equations
• Rényi entropy and improved equilibration rates to self-similarity for nonlinear diffusion equations
• The Concavity of Rényi Entropy Power
• Some inequalities satisfied by the quantities of information of Fisher and Shannon
• Non-uniform bound and finite time blow up for solutions to a drift–diffusion equation in higher dimensions
• Infinite time aggregation for the critical Patlak‐Keller‐Segel model in ℝ²
• Decay Estimates and Large Time Behavior of Solutions to the Drift-Diffusion System
• A Lyapunov functional for the evolution of solutions to the porous medium equation to self-similarity. I
• A Lyapunov functional for the evolution of solutions to the porous medium equation to self-similarity. II
• Logarithmic Sobolev Inequalities
• Logarithmic Sobolev Inequalities for the Heat-Diffusion Semigroup
• Exponential convergence toward equilibrium for homogeneous Fokker-Planck-type equations
• Asymptotic L^1-decay of solutions of the porous medium equation to self-similarity
• Decay Properties and Asymptotic Profiles of Bounded Solutions to a Parabolic System of Chemotaxis in Rn
• Asymptotic profile with the optimal convergence rate for a parabolic equation of chemotaxis in super-critical cases
• Finite-time blow-up for solutions to a degenerate drift-diffusion equation for a fast-diffusion case
• Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities

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