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Classical and Stochastic Laplacian Growth (Advances in Mathematical Fluid Mechanics),Used
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This monograph covers a multitude of concepts, results, and research topics originating from a classical movingboundary problem in two dimensions (idealized HeleShaw 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 infinitesize limit of ensembles of random matrices with complex eigenvalues; integrable hierarchies of differential equations and their spectral curves; classical and stochastic Lwner evolution and critical phenomena in twodimensional statistical models; weak solutions of hyperbolic partial differential equations of singularperturbation type; and resolution of singularities for compact Riemann surfaces with antiholomorphic 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 selfcontained resource. It is accessible to a wide readership, from beginner graduate students to researchers from various fields in natural sciences and mathematics.
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