Large-time behavior of a class of positive solutions of discrete equation Δu(n + k) = −p(n)u(n) in the critical case

2017 ◽  
Author(s):  
Jaromír Baštinec ◽  
Josef Diblík ◽  
Marie Klimešová
Keyword(s):  
Positive Solutions ◽  
Critical Case ◽  
Large Time ◽  
Large Time Behavior ◽  
Discrete Equation ◽  
Time Behavior

scholarly journals Analysis and simulation on dynamics of a partial differential system with nonlinear functional responses

2021 ◽  
Vol 26 (2) ◽  
pp. 293-314
Author(s):  
Yunfeng Jia
Keyword(s):  
Positive Solutions ◽  
Computational Analysis ◽  
Large Time ◽  
Food Resource ◽  
Reaction Diffusion ◽  
Large Time Behavior ◽  
Time Behavior ◽  
Functional Responses ◽  
Nonlinear Functional ◽  
Partial Differential System

We introduce a reaction–diffusion system with modified nonlinear functional responses. We first discuss the large-time behavior of positive solutions for the system. And then, for the corresponding steady-state system, we are concerned with the priori estimate, the existence of the nonconstant positive solutions as well as the bifurcations emitting from the positive constant equilibrium solution. Finally, we present some numerical examples to test the theoretical and computational analysis results. Meanwhile, we depict the trajectory graphs and spatiotemporal patterns to simulate the dynamics for the system. The numerical computations and simulated graphs imply that the available food resource for consumer is very likely not single.

scholarly journals Fujita type theorem for a class of coupled quasilinear convection–diffusion equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yanan Zhou ◽  
Yan Leng ◽  
Yuanyuan Nie
Keyword(s):  
Critical Case ◽  
Large Time ◽  
Blow Up ◽  
Type Theorem ◽  
Large Time Behavior ◽  
Diffusion Equations ◽  
Time Behavior ◽  
Convection Term ◽  
Diffusion Term ◽  
Convection Diffusion

AbstractIn this paper, we establish the Fujita type theorem for a homogeneous Neumann outer problem of the coupled quasilinear convection–diffusion equations and formulate the critical Fujita exponent. Besides, the influence of diffusion term, reaction term, and convection term on the global existence and the blow-up property of the problem is revealed. Finally, we discuss the large time behavior of the solution to the outer problem in the critical case and describe the asymptotic behavior of the solution.

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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