
ISSN:
1937-1632
eISSN:
1937-1179
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Discrete & Continuous Dynamical Systems - S
February 2020 , Volume 13 , Issue 2
Issue on analysis of cross-diffusion systems
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This paper presents a qualitative analysis of a model describing the time and space dynamics of a virus which migrates driven by chemotaxis. The initial-boundary value problem related to applications of the model to a real biological dynamics is studied in detail. The main result consists in the proof of global existence and asymptotic stability.
We investigate the parabolic-elliptic Keller-Segel model
in a bounded domain
We introduce a notion of generalized solvability which is consistent with the classical solution concept, and we show that whenever
In this paper we consider a
The paper should be viewed as complement of an earlier result in [
In this paper we study an anti-angiogenic therapy model that deactivates the tumor angiogenic factors. The model consists of four parabolic equations and considers the chemotaxis and a logistic law for the endothelial cells and several boundary conditions, some of them are non homogeneous. We study the parabolic problem, proving the existence of a unique global positive solution for positive initial conditions, and the stationary problem, justifying the existence of one real number, an eigenvalue of a certain problem, which determines if the semi-trivial solutions are stable or unstable and the existence of a coexistence state.
This paper presents global existence and asymptotic behavior of solutions to the chemotaxis-growth system
in a smoothly bounded domain
This paper deals with the quasilinear Keller-Segel system
in
We consider a parabolic-elliptic chemotaxis system generalizing
in bounded smooth domains
● solutions are global and bounded if
● solutions are global if
● close to given radially symmetric functions there are many initial data producing unbounded solutions if
In particular, if
This paper is concerned with a general fully parabolic Keller-Segel system, defined in a convex bounded and smooth domain
This paper deals with the two-species chemotaxis-competition system
where
In this article we consider a coupled system of differential equations to describe the evolution of a biological species. The system consists of two equations, a second order parabolic PDE of nonlinear type coupled to an ODE. The system contains chemotactic terms with constant chemotaxis coefficient describing the evolution of a biological species "
We obtain results concerning the bifurcation of constant steady states under the assumption
with growth terms
The current paper is devoted to the study of traveling wave solutions of the following parabolic-elliptic-elliptic chemotaxis systems,
where
for every
where
This paper considers the following parabolic-elliptic chemotaxis-growth system with nonlinear diffusion
under homogeneous Neumann boundary conditions for some constants
then the above system possesses a global bounded classical solution for any sufficiently smooth initial data. The results improve the results by Wang et al. (J. Differential Equations 256 (2014)) and generalize the results of Zheng (J. Differential Equations 259 (2015)) and Galakhov et al. (J. Differential Equations 261 (2016)).
In this paper we deal with the initial-boundary value problem for chemotaxis-fluid model involving more complicated nonlinear coupling term, precisely, the following self-consistent system
where
The novelty here is that both the effect of gravity (potential force) on cells and the effect of the chemotactic force on fluid is considered, which leads to the stronger coupling than usual chemotaxis-fluid model studied in the most existing literatures. To the best of our knowledge, there is no global solvability result on this chemotaxis-Navier-Stokes system in the past works. It is proved in this paper that global weak solutions exist whenever
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