Global Existence and Asymptotic Behavior for a Two-Species Chemotaxis-Competition System with Loop and Singular Sensitivity

Global existence and asymptotic behavior to a chemotaxis–consumption system with singular sensitivity and logistic source

This article deals with the chemotaxis model with singular sensitivity and logistic source under homogenous Neumann boundary condition in a smooth bounded domain , with and for all s>0 with . For , we show that the system admits a global classical solution that provides , and . Furthermore, for N=2, under the assumptions above, we obtain the boundedness and asymptotic behavior of solutions that provide , , and μ sufficiently large.

Global existence, boundedness and asymptotic behavior of classical solutions to a fully parabolic two-species chemotaxis-competition model with singular sensitivity

Global existence and asymptotic behavior in a two-species chemotaxis system with logistic source

This paper deals with the two-species Keller--Segel-Stokes system with competitive kinetics $(n_1)_t + u\cdot\nabla n_1 =\Delta n_1 - \chi_1\nabla\cdot(n_1\nabla c)+ \mu_1n_1(1- n_1 - a_1n_2)$, $(n_2)_t + u\cdot\nabla n_2 =\Delta n_2 - \chi_2\nabla\cdot(n_2\nabla c) + \mu_2n_2(1- a_2n_1 - n_2), c_t + u\cdot\nabla c =\Delta c - c + \alpha n_1 +\beta n_2$, $u_t= \Delta u + \nabla P+ (\gamma n_1 + \delta n_2)\nabla\phi$, $ \nabla\cdot u = 0$ under homogeneous Neumann boundary conditions in a bounded domain $\Omega \subset \mathbb{R}^3$ with smooth boundary. Many mathematicians study chemotaxis-fluid systems and two-species chemotaxis systems with competitive kinetics. However, there are not many results on coupled two-species chemotaxis-fluid systems which have difficulties of the chemotaxis effect, the competitive kinetics and the fluid influence. Recently, in the two-species chemotaxis-Stokes system, where $-c+\alpha n_1+\beta n_2$ is replaced with $-(\alpha n_1+\beta n_2)c$ in the above system, global existence and asymptotic behavior of classical solutions were obtained in the 3-dimensional case under the condition that $\mu_1,\mu_2$ are sufficiently large. Nevertheless, the above system has not been studied yet; we cannot apply the same argument as in the previous works because of lacking the $L^\infty$-information of $c$. The main purpose of this paper is to obtain global existence and stabilization of classical solutions to the above system in the 3-dimensional case under the largeness conditions for $\mu_1,\mu_2$.

Global existence and asymptotic behavior in a two-species chemotaxis system with signal production

In this paper we investigate the global existence and asymptotic behavior of a reaction diffusion system with degenerate diffusion arising in the modeling and the spatial spread of an epidemic disease.

This paper is concerned with global existence, uniqueness, and asymptotic behavior, as time tends to infinity, of weak solutions to nonlinear thermoviscoelastic systems with clamped boundary conditions. The constitutive assumptions for the Helmholtz free energy include the model for the study of phase transitions in shape memory alloys. To describe phase transitions between different configurations of crystal lattices, we work in a framework in which the strain u u belongs to L ∞ {L^\infty } . It is shown that for any initial data of (strain, velocity, absolute temperature) ( u 0 , v 0 , θ 0 ) ∈ L ∞ × W 0 1 , ∞ × H 1 \left ( {u_0}, {v_0}, {\theta _0} \right ) \in \\ {L^\infty } \times W_0^{1, \infty } \times {H^1} , there is a unique global solution ( u , v , θ ) ∈ C ( [ 0 , + ∞ ] ; L ∞ ) × C ( 0 , + ∞ ) ; W 0 1 , ∞ ) ∩ L ∞ ( [ 0 , + ∞ ) ; W 1 , ∞ ) × C ( [ 0 , + ∞ ) ; H 1 ) \left ( u, v, \theta \right ) \in C\left ( \left [ 0, + \infty \right ]; {L^\infty } \right ) \times C\left ( 0, + \infty \right ); \\ \left . W_0^{1, \infty } \right ) \cap {L^\infty }\left ( \left [ 0, + \infty ); {W^{1, \infty }} \right ) \times C\left ( \left [ 0, + \infty \right ); {H^1} \right ) \right . . Results concerning the asymptotic behavior as time goes to infinity are obtained.

Global existence, asymptotic behavior and blowup of solutions for a class of nonlinear wave equations with dissipative term

The global existence and asymptotic behavior of smooth solutions to the initial-boundary value problem for the 1-DLyumkisenergy transport model in semiconductor science is studied. When the boundary is insulated, the smooth solution of the problem converges to a stationary solution of the drift diffusion equations, exponentially fast ast→∞t \to \infty.

Global existence, asymptotic behavior and blow-up of solutions for coupled Klein–Gordon equations with damping terms

We are concerned with the global existence and asymptotic behavior of classical solutions to the Cauchy problem for the full compressible Euler equations with damping in $\mathbb R^3$. We prove the global existence of the classical solutions by the delica

Global existence and asymptotic behavior for a fractional differential equation

Global Existence and Asymptotic Behavior for the 3D Compressible Non–isentropic Euler Equations with Damping

Global existence, blow-up and asymptotic behavior of solutions for a class of p(x)-Choquard diffusion equations in [formula omitted