Spiral Waves : Linear and Nonlinear Theory / Bjö Sandstede and Arnd Scheel.

Format:

Book

Author/Creator:

Sandstede, Bjö, author.

Scheel, Arnd, 1966- author.

Series:

Memoirs of the American Mathematical Society ; Volume 285.

Memoirs of the American Mathematical Society Series ; Volume 285

Language:

English

Subjects (All):

Reaction-diffusion equations.

Spirals--Mathematics.

Spirals.

Waves--Mathematics.

Waves.

Physical Description:

1 online resource (138 pages)

Edition:

First edition.

Place of Publication:

Providence, RI : American Mathematical Society, [2023]

Summary:

"Spiral waves are striking self-organized coherent structures that organize spatiotemporal dynamics in dissipative, spatially extended systems. In this paper, we provide a conceptual approach to various properties of spiral waves. Rather than studying existence in a specific equation, we study properties of spiral waves in general reaction-diffusion systems. We show that many features of spiral waves are robust and to some extent independent of the specific model analyzed. To accomplish this, we present a suitable analytic framework, spatial radial dynamics, that allows us to rigorously characterize features such as the shape of spiral waves and their eigenfunctions, properties of the linearization, and finite-size effects. We believe that our framework can also be used to study spiral waves further and help analyze bifurcations, as well as provide guidance and predictions for experiments and numerical simulations. From a technical point of view, we introduce non-standard function spaces for the well-posedness of the existence problem which allow us to understand properties of spiral waves using dynamical systems techniques, in particular exponential dichotomies. Using these pointwise methods, we are able to bring tools from the analysis of one-dimensional coherent structures such as fronts and pulses to bear on these inherently two-dimensional defects"-- Provided by publisher.

Notes:

Description based on print version record.

Includes bibliographical references and index.

Other Format:

Print version: Sandstede, Bjö Spiral Waves: Linear and Nonlinear Theory

ISBN:

9781470474836

1470474832