Qualitative analysis of a parabolic–elliptic attraction–repulsion chemotaxis model with logistic source

2016 ◽  
Vol 09 (04) ◽  
pp. 1650051
Author(s):  
Haiyan Li ◽  
Jianguo Gao
Keyword(s):  
Fixed Point ◽  
Qualitative Analysis ◽  
Global Solution ◽  
Cell Mass ◽  
Logistic Source ◽  
Unique Global Solution ◽  
Chemotaxis Model ◽  
Initial Cell ◽  
Point Argument ◽  
Moser's Iteration

In this paper, we focus on the qualitative analysis of a parabolic–elliptic attraction–repulsion chemotaxis model with logistic source. Applying a fixed point argument, [Formula: see text]-estimate technique and Moser’s iteration, we derive that the model admits a unique global solution provided the initial cell mass satisfying [Formula: see text] for [Formula: see text] While for [Formula: see text], there are no restrictions on the initial cell mass and the result still holds.

Knudsen type group for time in ℝ and related Boltzmann type equations

2021 ◽  
pp. 2150072
Author(s):  
Jörg-Uwe Löbus
Keyword(s):  
Boundary Conditions ◽  
Global Solution ◽  
Physical Space ◽  
Type Equation ◽  
Collision Kernel ◽  
Unique Global Solution ◽  
Initial Value ◽  
Type Group ◽  
Diffusive Boundary ◽  
Diffusive Part

We consider certain Boltzmann type equations on a bounded physical and a bounded velocity space under the presence of both reflective as well as diffusive boundary conditions. We introduce conditions on the shape of the physical space and on the relation between the reflective and the diffusive part in the boundary conditions such that the associated Knudsen type semigroup can be extended to time [Formula: see text]. Furthermore, we provide conditions under which there exists a unique global solution to a Boltzmann type equation for time [Formula: see text] or for time [Formula: see text] for some [Formula: see text] which is independent of the initial value at time 0. Depending on the collision kernel, [Formula: see text] can be arbitrarily small.

scholarly journals Global solutions to nonlinear second order interval integrodifferential equations by fixed point in partially ordered sets

2018 ◽  
Vol 37 (4) ◽  
pp. 153-172
Author(s):  
Robab Alikhani ◽  
Fariba Bahrani
Keyword(s):  
Fixed Point ◽  
Global Solution ◽  
Existence And Uniqueness ◽  
Initial Conditions ◽  
Partially Ordered Sets ◽  
Second Order ◽  
Partial Ordering ◽  
Order Interval ◽  
Ordered Sets ◽  
Partially Ordered

In this paper, we prove the existence and uniqueness of global solution for second order interval valued integrodifferential equation with initial conditions admitting only the existence of a lower solution or an upper solution. In this study, in order to make the global solution on entire $[0,b]$, we use a fixed point in partially ordered sets on the subintervals of $[0,b]$ and obtain local solutions. Also, under weak conditions we show being well-defined a special kind of  H-difference involved in this work. Moreover, we compare the results of existence and uniqueness under consideration of two kind of partial ordering on fuzzy numbers.

THE INITIAL VALUE PROBLEM FOR THE DEEP BÉNARD CONVECTION EQUATIONS WITH DATA IN Lq

1996 ◽  
Vol 06 (02) ◽  
pp. 269-277 ◽  
Author(s):  
Z. CHARKI
Keyword(s):  
Fixed Point ◽  
Initial Value Problem ◽  
Existence And Uniqueness ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Bénard Convection ◽  
Benard Convection ◽  
Point Argument

A fixed point argument is used to prove the existence and uniqueness of solutions for the unsteady deep Bénard convection equations in [Formula: see text] for [Formula: see text].

scholarly journals GLOBAL SOLUTION FOR THE GENERALIZED ANISOTROPIC NAVIER–STOKES EQUATIONS WITH LARGE DATA

2015 ◽  
Vol 20 (2) ◽  
pp. 205-231 ◽  
Author(s):  
Daoyuan Fang ◽  
Bin Han
Keyword(s):  
Initial Data ◽  
Besov Space ◽  
Global Solution ◽  
Stokes Equations ◽  
Large Data ◽  
Navier Stokes ◽  
Unique Global Solution ◽  
Large Initial Data ◽  
Navier Stokes Equations ◽  
Anisotropic Besov Space

We are concerned with 3D incompressible generalized anisotropic Navier– Stokes equations with hyperdissipative term in horizontal variables. We prove that there exists a unique global solution for it with large initial data in anisotropic Besov space.

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