Mathematical challenges in the theory of chemotaxis (Q1790430)

scientific article; zbMATH DE number 6946306

Language	Label	Description	Also known as
English	Mathematical challenges in the theory of chemotaxis	scientific article; zbMATH DE number 6946306

Statements

instance of

scholarly article

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title

Mathematical challenges in the theory of chemotaxis (English)

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author

Piotr Biler

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published in

Annales Mathematicae Silesianae

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publication date

2 October 2018

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zbMATH Keywords

chemotaxis

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blowup of solutions

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global existence of solutions

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MaRDI profile type

Publication

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full work available at URL

https://doi.org/10.2478/amsil-2018-0004

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cites work

Q4007944

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The analysis and geometry of Hardy's inequality

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Existence, uniqueness and Lipschitz dependence for Patlak-Keller-Segel and Navier-Stokes in $\mathbb R^2$ with measure-valued initial data

0 references

Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues

0 references

The Cauchy problem and self-similar solutions for a nonlinear parabolic equation

0 references

Existence and nonexistence of solutions for a model of gravitational interaction of particles, III

0 references

Growth and accretion of mass in an astrophysical model

0 references

Q4225524

0 references

Q3531361

0 references

Global existence versus blow up for some models of interacting particles

0 references

On the parabolic-elliptic limit of the doubly parabolic Keller–Segel system modelling chemotaxis

0 references

Local criteria for blowup in two-dimensional chemotaxis models

0 references

Large mass self-similar solutions of the parabolic-parabolic Keller-Segel model of chemotaxis

0 references

Long time behavior of solutions of Nernst-Planck and Debye-Hückel drift-diffusion systems

0 references

Large global-in-time solutions of the parabolic-parabolic Keller-Segel system on the plane

0 references

Existence and nonexistence of solutions for a model of gravitational interaction of particles, II

0 references

Blowup of solutions to generalized Keller-Segel model

0 references

The $8\pi$-problem for radially symmetric solutions of a chemotaxis model in a disc

0 references

The 8π‐problem for radially symmetric solutions of a chemotaxis model in the plane

0 references

Optimal criteria for blowup of radial andN-symmetric solutions of chemotaxis systems

0 references

Morrey spaces norms and criteria for blowup in chemotaxis models

0 references

Large global-in-time solutions to a nonlocal model of chemotaxis

0 references

Existence and nonexistence of solutions for a model of gravitational interaction of particles, I

0 references

Existence of Solutions for the Keller–Segel Model of Chemotaxis with Measures as Initial Data

0 references

Functional inequalities, thick tails and asymptotics for the critical mass Patlak-Keller-Segel model

0 references

Infinite time aggregation for the critical Patlak‐Keller‐Segel model in ℝ2

0 references

Q3431715

0 references

Diffusion, attraction and collapse

0 references

Global solutions of some chemotaxis and angiogenesis system in high space dimension

0 references

Q5547841

0 references

Navier-stokes flow in r3with measures as initial vorticity and morrey spaces

0 references

Asymptotic behavior of type I blowup solutions to a parabolic-elliptic system of drift-diffusion type

0 references

Singularity patterns in a chemotaxis model

0 references

Chemotactic collapse for the Keller-Segel model

0 references

A user's guide to PDE models for chemotaxis

0 references

From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I

0 references

From 1970 until present: the Keller-Segel model in chemotaxis and its consequences. II

0 references

Global well-posedness for Keller-Segel system in Besov type spaces

0 references

On Explosions of Solutions to a System of Partial Differential Equations Modelling Chemotaxis

0 references

Scaling in nonlinear parabolic equations

0 references

Grow-Up Rate and Refined Asymptotics for a Two-Dimensional Patlak–Keller–Segel Model in a Disk

0 references

Initiation of slime mold aggregation viewed as an instability

0 references

The Keller-Segel system of parabolic-parabolic type with initial data in weak $L^{n/2}(\mathbb{R}^n)$ and its application to self-similar solutions

0 references

Finite time blow-up of the solution for a nonlinear parabolic equation of drift-diffusion type.

0 references

Small data in an optimal Banach space for the parabolic-parabolic and parabolic-elliptic Keller-Segel equations in the whole space

0 references

Q5446138

0 references

A sufficient condition for type I blowup in a parabolic-elliptic system

0 references

Blowup of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domains

0 references

Blow-up behavior of solutions to a parabolic-elliptic system on higher dimensional domains

0 references

Bounded and unbounded oscillating solutions to a parabolic-elliptic system in two dimensional space

0 references

Asymptotic stability of singular solution to nonlinear heat equation

0 references

Q3438091

0 references

Blowup Behavior of Radial Solutions to Jaeger-Luckhaus System in High Dimensional Domains

0 references

Morrey spaces and classification of global solutions for a supercritical semilinear heat equation in $\mathbb{R}^n$

0 references

Free energy and self-interacting particles

0 references

Analysis on Morrey Spaces and Applications to Navier-Stokes and Other Evolution Equations

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Identifiers

zbMATH Open document ID

1403.35300

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Mathematics Subject Classification ID

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10.2478/AMSIL-2018-0004

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Wikidata QID

Q129813367

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Sitelinks

Mathematics(1 entry)

mardi Publication:1790430