Titlebook: Nonlinear PDE’s in Condensed Matter and Reactive Flows; Henri Berestycki,Yves Pomeau Book 2002 Springer Science+Business Media Dordrecht 2

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P. Coullet,E. Risler,N. Vanderbergheicularly one pilot who, while he appears jaunty and carefree about his dangerous bombing missions, secretly becomes sick with fear in every mission. He conceals his fear from his men because he feels a responsibility to give them confidence, and he conceals it from his wife who is planning to leave

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A Two-Species Reaction-Diffusion Problem with One Static Reactant: The Case of Higher Order Kinetics.]). Models for reaction-diffusion processes involving two chemical species have a long history and a large literature, and the interested reader is referred to the articles (and their reference lists) cited at the end. In this set of notes we consider the long-time dynamics of a one-dimensional rea

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Instabilities and Nonlinear Patterns of Overdriven Detonations in Gasesare presented. An asymptotic solution to the reactive Euler equations is obtained in a “Newtonian limit” yielding a nonlinear integral-differential equation for the dynamics of the cellular front. The solution is valid for a general irreversible kinetics of the chemical heat release but is limited t

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On Some Reaction-Diffusion Systems with Nonlinear Diffusion Arising in Biologytical articles such as those of Alikakos [1], Masuda [10], Haraux and Youkana [6], Hoshino [7] and Kanel [9]. Their main results concern the well-posedness of the parabolic problems, .∞ bounds on the solutions which do not depend on time and a study of their large time behavior; it turns out that th

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Control of Weakly Blowing up Semilinear Heat Equationsions. We consider nonlinearities for which, in the absence of control, blow up arises..We prove that when the nonlinearity grows at infinity fast enough, due to the local (in space) nature of the blow up phenomena, the control may not avoid the blow up to occur for suitable initial data. This is don

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Spirals in Excitable Mediaregime where the wave tip rotates on a circle which is much larger than the width of the one-dimensional pulse. We describe an asymptotic analysis of spirals and of their counterparts, retracting waves, from this viewpoint, in the free boundary limit where the propagating excited region is bounded b

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Numerical Modelling of High Speed and Low Speed Combustion number of specific physical properties of combustion systems, which are extremely difficult to represent by discrete numerical approximations. This article explains three key problem areas that are relevant to premixed turbulent combustion and that are related to singular limit regimes of the under

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Overdetermined Elliptic Problems in Physicsry-value problems. Such situations appear for instance in fluid me- chanics and capillarity theory, theory of elasticity, electrostatics. Our goal here is to give an idea of how they have been treated mathematically.