scholarly journals Large Time Behavior in a Chemotaxis Model with Nonlinear General Diffusion for Tumor Invasion

2018 ◽  
Vol 61 (1) ◽  
pp. 37-80 ◽  
Author(s):  
Kentarou Fujie ◽  
Sachiko Ishida ◽  
Akio Ito ◽  
Tomomi Yokota
Keyword(s):  
Tumor Invasion ◽  
Large Time ◽  
Large Time Behavior ◽  
Time Behavior ◽  
Chemotaxis Model

Boundedness and large time behavior in a quasilinear chemotaxis model for tumor invasion

2018 ◽  
Vol 28 (07) ◽  
pp. 1413-1451 ◽  
Author(s):  
Dan Li ◽  
Chunlai Mu ◽  
Pan Zheng
Keyword(s):  
Tumor Invasion ◽  
Large Time ◽  
System Modeling ◽  
Neumann Boundary ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Large Time Behavior ◽  
Time Behavior ◽  
The Matrix ◽  
Initial Boundary Value

This paper deals with the quasilinear chemotaxis system modeling tumor invasion [Formula: see text] under homogenous Neumann boundary conditions in a smoothly convex bounded domain [Formula: see text] [Formula: see text], where [Formula: see text] is a given function satisfying [Formula: see text] for all [Formula: see text] with [Formula: see text] and [Formula: see text]. Here the matrix-valued function [Formula: see text] fulfills [Formula: see text] for all [Formula: see text] with some [Formula: see text] and [Formula: see text]. It is shown that for all reasonably regular initial data, a corresponding initial-boundary value problem for this system possesses a globally defined weak solution under some assumptions. Based on this boundedness property, it can finally be proved that in the large time limit, any such solution approaches the spatially homogenous equilibrium [Formula: see text] in an appropriate sense, where [Formula: see text], [Formula: see text] and [Formula: see text] provided that merely [Formula: see text] on [Formula: see text]. To the best of our knowledge, there are the first results on boundedness and asymptotic behavior of the system.

scholarly journals Global well-posedness of the full compressible Hall-MHD equations

2021 ◽  
Vol 10 (1) ◽  
pp. 1235-1254
Author(s):  
Qiang Tao ◽  
Canze Zhu
Keyword(s):  
Global Solution ◽  
Large Time ◽  
Initial Temperature ◽  
Large Time Behavior ◽  
Initial Energy ◽  
Mhd Equations ◽  
Well Posedness ◽  
Time Behavior ◽  
Magnetohydrodynamic Flows ◽  
Hall Mhd

Abstract This paper deals with a Cauchy problem of the full compressible Hall-magnetohydrodynamic flows. We establish the existence and uniqueness of global solution, provided that the initial energy is suitably small but the initial temperature allows large oscillations. In addition, the large time behavior of the global solution is obtained.

Large Time Behavior of Solutions to One Nonlinear Integro-Differential Equation

2008 ◽  
Vol 15 (3) ◽  
pp. 531-539
Author(s):  
Temur Jangveladze ◽  
Zurab Kiguradze
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Boundary Conditions ◽  
Large Time ◽  
Dirichlet Boundary ◽  
Large Time Behavior ◽  
Dirichlet Boundary Conditions ◽  
Time Behavior ◽  
Integro Differential Equation ◽  
Homogeneous Data

Abstract Large time behavior of solutions to the nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance is studied. The rate of convergence is given, too. Dirichlet boundary conditions with homogeneous data are considered.

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