Propagating Terraces and the Dynamics of Front-Like Solutions of Reaction-Diffusion Equations on $\mathbb {R}$, Peter Polacik

Автор: Joachim K Krieger
Название: On Stability of Type II Blow Up for the Critical Nonlinear Wave Equation in $\mathbb {R}^{3+1}$
ISBN: 147044299X ISBN-13(EAN): 9781470442996
Издательство: Mare Nostrum (Eurospan)
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Описание: The author shows that the finite time type II blow up solutions for the energy critical nonlinear wave equation $ \Box u = -u^5 $ on $\mathbb R^3+1$ constructed in Krieger, Schlag, and Tataru (2009) and Krieger and Schlag (2014) are stable along a co-dimension three manifold of radial data perturbations in a suitable topology, provided the scaling parameter $\lambda (t) = t^-1-\nu $ is sufficiently close to the self-similar rate, i. e. $\nu >0$ is sufficiently small. Our method is based on Fourier techniques adapted to time dependent wave operators of the form $ -\partial _t^2 + \partial _r^2 + \frac 2r\partial _r +V(\lambda (t)r) $ for suitable monotone scaling parameters $\lambda (t)$ and potentials $V(r)$ with a resonance at zero.

Автор: Oleg Kupervasser
Название: Pole Solutions for Flame Front Propagation
ISBN: 3319188445 ISBN-13(EAN): 9783319188447
Издательство: Springer
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Цена: 6986.00 р.
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Описание: This book deals with solving mathematically the unsteady flame propagation equations. Premixed flames and filtration combustion have remarkable properties: the complex nonlinear integro-differential equations for these problems have exact analytical solutions described by the motion of poles in a complex plane.