2 edition of **Travelling fronts and wave-trains in reaction-diffusion equations** found in the catalog.

Travelling fronts and wave-trains in reaction-diffusion equations

Alison Lindsey Kay

- 43 Want to read
- 12 Currently reading

Published
**1999**
by typescript in [s.l.]
.

Written in English

**Edition Notes**

Thesis (Ph.D.) - University of Warwick, 1999.

Statement | Alison Lindsey Kay. |

The Physical Object | |
---|---|

Pagination | 186p. |

Number of Pages | 186 |

ID Numbers | |

Open Library | OL19460903M |

This site uses cookies. By continuing to use this site you agree to our use of cookies. To find out more, see our Privacy and Cookies policy. traveling front. Traveling fronts (or wave fronts) are solutions to equations (), of the form u(x;t) = ’(x ct); where c2R is the speed of the wave and ’: R!R is the wave pro le function. For pattern formation problems it is natural to consider in nite domains and to neglect the in uence of boundary conditions.

Buy Travelling Waves in Nonlinear Diffusion-Convection Reaction (Progress in Nonlinear Differential Equations and Their Applications) on FREE SHIPPING on qualified orders. Figure 1: A schematic illustration of the qualitative form of (a) a sharp-front travelling wave, and (b) a smooth-front travelling wave. 2. Travelling Wave Fronts for Equations with Degenerate Dif-fusion Wave front solutions of reaction-diffusion equations with degenerate nonlinear diffusion were ﬁrst studied thirty years ago [1, 30].

Reaction-Diffusion Fronts in Periodically Layered Media (with G. Papanicolaou), J. Stat. Physics, Vol. 63, Nos. 5/6, , pp Existence and Stability of Travelling Waves in Periodic Media Governed by a Bistable Nonlinearity, Journal of Dynamics and Differential Equations, 3(4), , pp eralization of the FitzHugh-Nagumo equations. This reaction-diffusion model has the same ﬂavor as the semiconductor system but trades the complicated trigonometric nonlinearity for a simpler cubic form. In addition to the well known traveling fronts and pulses we found oscillating and stationary domains.

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Reaction–diffusion systems are mathematical models which correspond to several physical phenomena. Travelling fronts and wave-trains in reaction-diffusion equations book The most common is the change in space and time of the concentration of one or more chemical substances: local chemical reactions in which the substances are transformed into each other, and diffusion which causes the substances to spread out over a surface in space.

In recent years, traveling wave solutions of reaction-diffusion equations have attracted increasing interest (see e.g., [6,7,28,18, 27, 9,10,8]). It is well known that traveling wave is one kind.

In this work, we limit our review to scalar reaction–diffusion equations and concentrate on monostable and bistable front solutions. More complex spatio-temporal structures have been studied for higher-order reaction–diffusion systems (see, for example, [20–24]).Cited by: 2.

In the one-dimensional space, traveling wave solutions of parabolic differential equations have been widely studied and well characterized. Recently, the mathematical study on higher-dimensional traveling fronts has attracted a lot of attention and many new types of nonplanar traveling waves have been observed for scalar reaction-diffusion equations with various by: () travelling wave solutions for doubly degenerate reaction–diffusion equations.

The ANZIAM Journal() Multiple positive solutions to a singular boundary value problem for a superlinear Emden–Fowler by: Periodic wave trains are the generic solution from for oscillatory reaction-diffusion equations in one space dimension.

It has been shown previously that invasive wavefronts generate behind them a wave train with a different speed from that. [1] Matthieu Alfaro, Jérôme Coville and Gaël Raoul, Travelling waves in a nonlocal reaction-diffusion equation as a model for a population structured by a space variable and a phenotypical trait, ().Google Scholar [2] Tobias Back, Jochen G.

Hirsch, Kristina Szabo and Achim Gass, Failure to demonstrate peri-infarct depolarizations by repetitive mr diffusion imaging in acute human.

The existence and comparison theorem of solutions is first established for the quasi-monotone delayed reaction-diffusion equations on R by appealing to the theory of abstract functional differential equations. The global asymptotic stability, Liapunov stability, and uniqueness of traveling wave solutions are then proved by the elementary super- and subsolution comparison and squeezing methods.

In this paper we study the existence and non-existence of traveling front solutions in multistable reaction-di usion equations. If this equation has a traveling front solution, a perturbed equation also has a traveling front solution.

We study how the speed and the traveling pro le. Propagation speed of travelling fronts in non local Nonlocal reaction-diffusion equations; Propagation speed 1. Introduction In this article, we are concerned with variational formulas characterizingthe speedc of travellingfrontsu arisingin the study of a nonlocal reaction–diffusion model.

More see the excellent book of Murray [23]and. Reaction-diffusion equations describe the behaviour of a large range of chemical systems where diffusion of material competes with the production of that material by some form of chemical reaction.

Many other kinds of systems are described by the same type of relation. Thus systems where heat (or fluid) is produced and diffuses away from the heat (or fluid) production site are described by the.

In the paper, we derive a delayed reaction-diffusion equations, which describes a multi-species Predator-prey system. By coupling the perturbation approach with the method of upper and lower solutions, we prove that the traveling wave fronts exist and appear monotone, which connect the zero solution with the positive steady state.

Finally, we draw a conclusion to point out that the existence. of traveling pulses in the FitzHugh{Nagumo equation. The arguments of these authors use the fact that eLis a compact perturbation of eL 0, where L 0 is the linearization of the partial di erential operator at q = q+, which is a constant-coe cient operator.

If q 6= q+, the traveling wave is a front. Fronts in the FitzHugh{Nagumo equation have. GENERALIZED TRAVELLING WAVES FOR REACTION-DIFFUSION EQUATIONS 3 Pulsating travelling fronts, periodic media.

Another important ex-ample of travelling fronts is for heterogeneous equations of the type () u t = ∇(A(x)∇u)+q(x)∇u+f(x,u) in RN, where the uniformly elliptic matrix ﬁeld A, the vector ﬁeld qand the function f.

These equations often take the form of systems of nonlinear parabolic partial d- ferential equations, or reaction-diffusion equations, when there is diffusion of chemical substances involved. A good overview of this endeavor can be had by re- ing the two volumes by R.

Aris (), who himself was one of the main contributors to the theory. The existence of travelling wave fronts for nonlocal reaction-diffusion systems with delays is established by using Schauder’s fixed point theorem and upper-lower solution technique.

"Traveling front solutions in reaction-diffusion equations" (book) submitted Masaharu Taniguchi "Convex compact sets in $\mathbb{R}^{N-1}$ give traveling fronts of cooperation-diffusion systems in $\mathbb{R}^{N}$" Journal of Differential Equations (), pp.

Masaharu Taniguchi. Poláčik, Spatial trajectories and convergence to traveling fronts for bistable reaction-diffusion equations, Contributions to nonlinear differential equations and systems, A tribute to Djairo Guedes de Figueiredo on the occasion of his 80th Birthday (A.N.

Carvalho, B. Ruf, E.M. Moreira dos Santos, S.H. Soares, and T. Cazenave, eds. Section I deals with reaction-diffusion equations, and in it are described both the work of C.

Jones, on the stability of the travelling wave for the Fitz-Hugh-Nagumo equations, and symmetry-breaking bifurcations. Section II deals with some recent results in shock-wave theory. existence of wave fronts is independent of the size of the delay.

It should be mentioned that traveling wave solutions for reaction-diffusion equations without delay have been extensively studied in the literature. The recent book review by Gardner () and the monographs by Fife (), Britton (), Murray (), and Volpert et al.

(). Figure 1: A schematic illustration of the qualitative form of (a) a sharp-front travelling wave, and (b) a smooth-front travelling wave.

2. Travelling Wave Fronts for Equations with Degenerate Dif-fusion Wave front solutions of reaction-diffusion equations with degenerate nonlinear diffusion were rst studied thirty years ago [1, 30].35Q92, 37N25, 92Bxx Mathematical Biology Quiescent states Population dynamics Epidemic models Reaction-diffusion equations Stability and Bifurcations Travelling Fronts .S~nchez-Gardufio and Maini [17] showed that for a large family of reaction-diffusion equations with degenerate nonlinear diffusion, including (2), there is a travelling wave of sharp-front type for exactly one value of the wave speed, c* say.

For c travelling waves, while.