Nonlinear Diffusive Waves
By (author) P. L. Sachdev
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Nonlinear Diffusive Waves by P. L. Sachdev
Book DescriptionThis monograph deals with Burgers' equation and its generalisations. Such equations describe a wide variety of nonlinear diffusive phenomena, for instance, in nonlinear acoustics, laser physics, plasmas and atmospheric physics. The Burgers equation also has mathematical interest as a canonical nonlinear parabolic differential equation that can be exactly linearised. It is closely related to equations that display soliton behaviour and its study has helped elucidate other such nonlinear behaviour. The approach adopted here is applied mathematical. The author discusses fully the mathematical properties of standard nonlinear diffusion equations, and contrasts them with those of Burgers' equation. Of particular mathematical interest is the treatment of self-similar solutions as intermediate asymptotics for a large class of initial value problems whose solutions evolve into self-similar forms. This is achieved both analytically and numerically.
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Book DetailsISBN: 9780521093033
(228mm x 152mm x 15mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 8-Jan-2009
Country of Publication: United Kingdom
Books By Author P. L. Sachdev
Large Time Asymptotics for Solutions of Nonlinear Partial Differential Equations, Hardback (November 2009)» View all books by P. L. Sachdev
The goals of this text are to prove or disprove the solution of reduced nonlinear ODE's by different analytic methods, and to show that these solutions are intermediate asymptotics of a class of initial/boundary conditions arising from physical considerations.
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