Book Review: Traveling wave solutions of parabolic systems

Abstract

446BOOK REVIEWS the predecessor volume [6] at hand. Many further results are given as exercises, with solutions or references.Besides, I found no serious lacuna in the index and very few misprints in the book, none of them bothersome. (At the author's request, I mention that the remark on page 274 should be deleted.) As in [5 and 6], for which Helgason received the 1988 Steele Prize for expository writing, the style is very fluent and pleasant, conducting the reader at a regular pace. I think the present book will be a most valuable (and reasonably priced) reference for anyone interested in Radon transforms and analysis on semisimple Lie groups. 4. V.

Perron Theorem in the monotone iteration method for traveling waves in delayed reaction–diffusion equations

“…As usual we look for traveling wave solutions of (10) in the form u( (10) leads to the following wave equation…”

“…Traveling waves, although are a classical topic in applied mathematics, remain a driving force in the study of (1). We refer the reader to [10,30] which contain many surveys on methods used to study traveling waves in parabolic differential equations. Note that when delay is introduced, most methods would fail if they are not modified appropriately (see e.g.…”

Traveling waves for a time delayed Newtonian filtration equation

“…From the physical point of view, as one of the examples, the traveling wave can be used to describe transition process from one equilibrium to another, which usually forgets their initial conditions and the properties of the medium itself [16]. The early important contribution on traveling waves was made in [17,18], since then, the investigation on traveling wave phenomena has played an important role in the qualitative theory of solutions to reaction-diffusion systems [19]. Please see for example [20,21] and the references therein for much research about the traveling waves of reaction-diffusion equations.…”

Travelling Wave Solutions in Delayed Reaction Diffusion Systems with Partial Monotonicity

“…For reaction diffusion systems without time delay, existence of travelling wave solutions have been extensively and intensively studied, see Gardner [3] , Fife [2] , Britton [1] , Murray [9] , Volpert et al [17] and so on. However, little is known on travelling wave solutions for reaction diffusion systems with time delay.…”