Classical and stochastic Laplacian growth [electronic resource] / Björn Gustafsson, Razvan Teodorescu, Alexander Vasil'ev.

Classical and stochastic Laplacian growth [electronic resource] / Björn Gustafsson, Razvan Teodorescu, Alexander Vasil'ev.

9783319082875 electronic book
3319082876 electronic book
9783319082868
3319082868

Cham : Birkhäuser, 2014.

English

1 online resource (xiv, 317 pages) : illustrations.

10.1007/978-3-319-08287-5 doi

TA357

620.1/06

This monograph covers a multitude of concepts, results, and research topics originating from a classical moving-boundary problem in two dimensions (idealized Hele-Shaw flows, or classical Laplacian growth), which has strong connections to many exciting modern developments in mathematics and theoretical physics. Of particular interest are the relations between Laplacian growth and the infinite-size limit of ensembles of random matrices with complex eigenvalues; integrable hierarchies of differential equations and their spectral curves; classical and stochastic Löwner evolution and critical phenomena in two-dimensional statistical models; weak solutions of hyperbolic partial differential equations of singular-perturbation type; and resolution of singularities for compact Riemann surfaces with anti-holomorphic involution. The book also provides an abundance of exact classical solutions, many explicit examples of dynamics by conformal mapping as well as a solid foundation of potential theory. An extensive bibliography covering over twelve decades of results and an introduction rich in historical and biographical details complement the eight main chapters of this monograph. Given its systematic and consistent notation and background results, this book provides a self-contained resource. It is accessible to a wide readership, from beginner graduate students to researchers from various fields in natural sciences and mathematics.

Includes bibliographical references and index.

Access limited to authorized users.

Advances in mathematical fluid mechanics.

Print version: 9783319082868

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