Large time behavior of the broadwell model of a discrete velocity gas with specularly reflective boundary conditions

1990 ◽  
Vol 111 (4) ◽  
pp. 323-342 ◽  
Author(s):  
M. Slemrod
Keyword(s):  
Boundary Conditions ◽  
Large Time ◽  
Large Time Behavior ◽  
Time Behavior ◽  
Discrete Velocity

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.

scholarly journals Global dynamics in a competitive two-species and two-stimuli chemotaxis system with chemical signalling loop

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Rong Zhang ◽  
Liangchen Wang
Keyword(s):  
Boundary Conditions ◽  
Bounded Domain ◽  
Large Time ◽  
Neumann Boundary ◽  
Rates Of Convergence ◽  
Large Time Behavior ◽  
Global Dynamics ◽  
Time Behavior ◽  
Chemical Signalling ◽  
Chemotaxis System

<p style='text-indent:20px;'>This paper deals with the following competitive two-species and two-stimuli chemotaxis system with chemical signalling loop</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{eqnarray*} \left\{ \begin{array}{llll} u_t = \Delta u-\chi_1\nabla\cdot(u\nabla v)+\mu_1 u(1-u-a_1w),\, x\in \Omega,\, t&gt;0,\\ 0 = \Delta v-v+w,\,x\in\Omega,\, t&gt;0,\\ w_t = \Delta w-\chi_2\nabla\cdot(w\nabla z)-\chi_3\nabla\cdot(w\nabla v)+\mu_2 w(1-w-a_2u), \,x\in \Omega,\,t&gt;0,\\ 0 = \Delta z-z+u, \,x\in\Omega,\, t&gt;0, \end{array} \right. \end{eqnarray*} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>under homogeneous Neumann boundary conditions in a bounded domain <inline-formula><tex-math id="M1">\begin{document}$ \Omega\subset \mathbb{R}^n $\end{document}</tex-math></inline-formula> with <inline-formula><tex-math id="M2">\begin{document}$ n\geq1 $\end{document}</tex-math></inline-formula>, where the parameters <inline-formula><tex-math id="M3">\begin{document}$ a_1,a_2 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M4">\begin{document}$ \chi_1, \chi_2, \chi_3 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M5">\begin{document}$ \mu_1, \mu_2 $\end{document}</tex-math></inline-formula> are positive constants. We first showed some conditions between <inline-formula><tex-math id="M6">\begin{document}$ \frac{\chi_1}{\mu_1} $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M7">\begin{document}$ \frac{\chi_2}{\mu_2} $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M8">\begin{document}$ \frac{\chi_3}{\mu_2} $\end{document}</tex-math></inline-formula> and other ingredients to guarantee boundedness. Moreover, the large time behavior and rates of convergence have also been investigated under some explicit conditions.</p>

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.

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