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Existence of pulsating waves in a model of flames in sprays

Peter Constantin, Komla Domelevo, Jean-Michel Roquejoffre, Lenya Ryzhik (2006)

Journal of the European Mathematical Society

A one-dimensional system describing the propagation of low Mach number flames in sprays is studied. We show that pulsating waves may exist when the droplet distribution in the unburnt region is spatially periodic. The range of possible propagation speeds may be either bounded or unbounded, depending on the threshold temperatures of the burning and vaporization rates.

Existence of solution to nonlinear boundary value problem for ordinary differential equation of the second order in Hilbert space

Eva Rovderová (1992)

Mathematica Bohemica

In this paper we deal with the boundary value problem in the Hilbert space. Existence of a solutions is proved by using the method of lower and upper solutions. It is not necessary to suppose that the homogeneous problem has only the trivial solution. We use some results from functional analysis, especially the fixed-point theorem in the Banach space with a cone (Theorem 4.1, [5]).

Existence of solutions for a model of self-gravitating particles with external potential

Andrzej Raczyński (2004)

Banach Center Publications

We study the existence of solutions to a nonlinear parabolic equation describing the temporal evolution of a cloud of self-gravitating particles with a given external potential. The initial data are in spaces of (generalized) pseudomeasures. We prove existence of local and global-in-time solutions, and also a kind of stability of global solutions.

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