scholarly journals Traveling wave solutions of a 3-component reaction-diffusion model in smoldering combustion

2012 ◽  
Vol 11 (1) ◽  
pp. 275-305 ◽  
Author(s):  
Kota Ikeda ◽  
◽  
Masayasu Mimura ◽  
Keyword(s):  
Diffusion Model ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Smoldering Combustion ◽  
Wave Solutions ◽  
Reaction Diffusion Model

scholarly journals TRAVELING WAVE SOLUTIONS IN A STAGE-STRUCTURED DELAYED REACTION-DIFFUSION MODEL WITH ADVECTION

2015 ◽  
Vol 20 (2) ◽  
pp. 168-187
Author(s):  
Liang Zhang ◽  
Huiyan Zhao
Keyword(s):  
Diffusion Model ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Stage Structure ◽  
Delayed Reaction ◽  
Wave Solutions ◽  
Reaction Diffusion Model ◽  
Travelling Fronts ◽  
Appl Math

We investigate a stage-structured delayed reaction-diffusion model with advection that describes competition between two mature species in water flow. Time delays are incorporated to measure the time lengths from birth to maturity of the populations. We show there exists a finite positive number c∗ that can be characterized as the slowest spreading speed of traveling wave solutions connecting two mono-culture equilibria or connecting a mono-culture with the coexistence equilibrium. The model and mathematical result in [J.F.M. Al-Omari, S.A. Gourley, Stability and travelling fronts in Lotka–Volterra competition models with stage structure, SIAM J. Appl. Math. 63 (2003) 2063–2086] are generalized.

scholarly journals Traveling Wave Solutions of a Four Dimensional Reaction-Diffusion Model for Porcine Reproductive and Respiratory Syndrome with Time Dependent Infection Rate

Computation ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 30
Author(s):  
Jeerawan Suksamran ◽  
Yongwimon Lenbury ◽  
Sanoe Koonprasert
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Growing Pigs ◽  
Respiratory Syndrome Virus ◽  
Swine Industry ◽  
Reaction Diffusion Model ◽  
Spatial Dimensions ◽  
Tangent Method ◽  
Spatial Transmission

Porcine reproductive and respiratory syndrome virus (PRRSV) causes reproductive failure in sows and respiratory disease in piglets and growing pigs. The disease rapidly spreads in swine populations, making it a serious problem causing great financial losses to the swine industry. However, past mathematical models used to describe the spread of the disease have not yielded sufficient understanding of its spatial transmission. This work has been designed to investigate a mathematical model for the spread of PRRSV considering both time and spatial dimensions as well as the observed decline in infectiousness as time progresses. Moreover, our model incorporates into the dynamics the assumption that some members of the infected population may recover from the disease and become immune. Analytical solutions are derived by using the modified extended hyperbolic tangent method with the introduction of traveling wave coordinate. We also carry out a stability and phase analysis in order to obtain a clearer understanding of how PRRSV spreads spatially through time.

scholarly journals Some New Traveling Wave Solutions of the Nonlinear Reaction Diffusion Equation by Using the Improved (G′/G)-Expansion Method

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Hasibun Naher ◽  
Farah Aini Abdullah
Keyword(s):  
Diffusion Equation ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Expansion Method ◽  
Reaction Diffusion Equation ◽  
Wave Solutions ◽  
Nonlinear Reaction ◽  
Nonlinear Reaction Diffusion Equation ◽  
Constant Coefficients

We construct new exact traveling wave solutions involving free parameters of the nonlinear reaction diffusion equation by using the improved (G′/G)-expansion method. The second-order linear ordinary differential equation with constant coefficients is used in this method. The obtained solutions are presented by the hyperbolic and the trigonometric functions. The solutions become in special functional form when the parameters take particular values. It is important to reveal that our solutions are in good agreement with the existing results.

Sign in / Sign up

Export Citation Format

Share Document