EurekaMag.com logo
+ Translate

The long time behavior of the solution to a nonlinear diffusion problem in population genetics and combustion


, : The long time behavior of the solution to a nonlinear diffusion problem in population genetics and combustion. Journal of Theoretical Biology 104(4): 473-484

The Fisher or Kolmogoroff-Petrovsky-Piscounoff equation exemplifies wave-like phenomena occurring in population genetics and combustion. An extension of this equation was proposed and closed form traveling wave, stationary and symmetric solutions were obtained. Employing the transformation properties of the extended equation, 2 integral invariants for the problem are obtained and 2 Lyapunov functionals, which characterize the evolution of the profile to a uniformly propagating traveling wave, are constructed. A generalization of this modified Fisher equation is proposed and its integral invariants, traveling wave solutions and wave speeds were obtained, as well as the Lyapunov functionals which describe its asymptotic evolution.

(PDF 0-2 workdays service)

Accession: 006712070

Submit PDF Full Text: Here


Submit PDF Full Text

No spam - Every submission is manually reviewed

Due to poor quality, we do not accept files from Researchgate

Submitted PDF Full Texts will always be free for everyone
(We only charge for PDFs that we need to acquire)

Select a PDF file:
Close
Close

Related references

Langlais, M., 1988: Large time behavior in a nonlinear age-dependent population dynamics problem with spatial diffusion. In this work we analyze the large time behavior in a nonlinear model of population dynamics with age-dependence and spatial diffusion. We show that when t----+ infinity either the solution of our problem goes to 0 or it stabilizes to a nontrivial...

Newman, W.I., 1980: Some exact solutions to a non-linear diffusion problem in population genetics and combustion. The Fisher or Kolmogoroff-Petrovsky-Piscounoff equation has had wide application in describing phenomena occurring in population genetics and combustion. An extension of this equation was proposed and closed form traveling wave, stationary and sym...

Chen, R.-zhao.; Li, J.-quan.; Fu, J.., 2001: Existence of the generalized solution for the nonlinear age-dependnet population diffusion equation. Journal of Northeast Normal University Natural Sciences Edition. September 20; 333: 3-13

Vlad, M.Ovidiu.; Moran, F.; Tsuchiya, M.; Cavalli-Sforza, L.Luca.; Oefner, P.J.; Ross, J., 2002: Neutrality condition and response law for nonlinear reaction-diffusion equations, with application to population genetics. We study a general class of nonlinear macroscopic evolution equations with "transport" and "reaction" terms which describe the dynamics of a species of moving individuals (atoms, molecules, quasiparticles, organisms, etc.). We...

Grigori Chapiro; Alexei A.M.ilybaev; Aparecido J. de Souza; Dan Marchesin; Johannes Bruining, 2012: Asymptotic approximation of long-time solution for low-temperature filtration combustion. There is a renewed interest in using combustion for the recovery of medium viscosity oil. We consider the combustion process when air is injected into the porous medium containing some fuel and inert gas. Commonly the reaction rate is negligible a...

Azevedo, C.A.V. de; Merkley, G.P.; Walker, W.R., 1997: Nonlinear optimization in the real-time solution of the inverse furrow irrigation problem. A computer nonlinear optimization model was developed to interact upon a kinematic-wave hydraulic model to obtain the Kostiakov-Lewis parameters from measured advance data (furrow irrigation inverse problem). This model is part of a computer progr...

Jorne J.; Safriel U.N., 1979: Linear and nonlinear diffusion models applied to the behavior of a population of an inter tidal snail. The flux and continuity equations are presented for a non-linear diffusion of populations. The generalized diffusion-reaction equations are presented for both random and biased diffusion, where a bias is introduced toward the existing gradient of...

Sornette Didier; Sornette Anne; Romanowicz Barbara; Rundle John, 1994: On scaling relations for large earthquakes by B. Romanowicz and J. B. Rundle, from the perspective of a recent nonlinear diffusion equation linking short-time deformation to long-time tectonics; discussion and reply. Bulletin of the Seismological Society of America 84(5): 1679-1684

Lorkovie, Z.; Herman, xC., 1961: The solution of a long outstanding problem in the genetics of dimorphism in Colias. Journal of the Lepidopterist's Society, 15: 43-55

Gutierrez, J.B.; Lai, M-Jun.; Slavov, G., 2015: Bivariate spline solution of time dependent nonlinear PDE for a population density over irregular domains. We study a time dependent partial differential equation (PDE) which arises from classic models in ecology involving logistic growth with Allee effect by introducing a discrete weak solution. Existence, uniqueness and stability of the discrete weak...