A logistic type equation in RN with a nonlocal reaction term via bifurcation method

2021 ◽  
Vol 493 (1) ◽  
pp. 124532
Author(s):  
Manuel Delgado ◽  
Mónica Molina-Becerra ◽  
Antonio Suárez
Keyword(s):  
Type Equation ◽  
Bifurcation Method ◽  
Reaction Term ◽  
Nonlocal Reaction

scholarly journals Bounded Traveling Wave Solutions and Their Relations for the Generalized HD Type Equation

2016 ◽  
Vol 2016 ◽  
pp. 1-15
Author(s):  
Qing Meng ◽  
Bin He
Keyword(s):  
Solitary Wave ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Sufficient Conditions ◽  
Traveling Wave Solutions ◽  
Type Equation ◽  
Periodic Wave ◽  
Point Of View ◽  
Bifurcation Method ◽  
Wave Solutions

The generalized HD type equation is studied by using the bifurcation method of dynamical systems. From a dynamic point of view, the existence of different kinds of traveling waves which include periodic loop soliton, periodic cusp wave, smooth periodic wave, loop soliton, cuspon, smooth solitary wave, and kink-like wave is proved and the sufficient conditions to guarantee the existence of the above solutions in different regions of the parametric space are given. Also, all possible exact parametric representations of the bounded waves are presented and their relations are stated.

scholarly journals Bifurcation and Solitary-Like Solutions for Compound KdV-Burgers-Type Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Yin Li ◽  
Ruiying Wei ◽  
Guoming Jian
Keyword(s):  
Dynamical Systems ◽  
Type Equation ◽  
Trigonometric Function ◽  
Hyperbolic Function ◽  
Bifurcation Method ◽  
Dynamical Characteristics ◽  
Hyperbolic Function Solutions ◽  
Trigonometric Function Solutions ◽  
Ode Method ◽  
Parameter Condition

Firstly, based on the improved sub-ODE method and the bifurcation method of dynamical systems, we investigate the bifurcation of solitary waves in the compound KdV-Burgers-type equation. Secondly, numbers of solitary patterns solutions are given for each parameter condition and numerical simulations are used to display the dynamical characteristics. Finally, we obtain twelve solitary patterns solutions under some parameter conditions, such as the trigonometric function solutions and the hyperbolic function solutions.

scholarly journals On a model of a population with variable motility

2015 ◽  
Vol 25 (10) ◽  
pp. 1961-2014 ◽  
Author(s):  
Olga Turanova
Keyword(s):  
Diffusion Equation ◽  
Long Range ◽  
Viscosity Solutions ◽  
Jacobi Equation ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Reaction Term ◽  
Long Time ◽  
Nonlocal Reaction ◽  
Hamilton Jacobi Equation

We study a reaction–diffusion equation with a nonlocal reaction term that models a population with variable motility. We establish a global supremum bound for solutions of the equation. We investigate the asymptotic (long-time and long-range) behavior of the population. We perform a certain rescaling and prove that solutions of the rescaled problem converge locally uniformly to zero in a certain region and stay positive (in some sense) in another region. These regions are determined by two viscosity solutions of a related Hamilton–Jacobi equation.

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