Nonlinear Diffusion Equations and their Equilibrium States, No. 3 (Progress in Nonlinear Differential Equations and Their Applications) - Hardcover

Hardcover

ISBN 10: 0817635319 ISBN 13: 9780817635312

Publisher: Birkhäuser, 1991

Synopsis

Nonlinear diffusion equations have held a prominent place in the theory of partial differential equations, both for the challenging and deep math­ ematical questions posed by such equations and the important role they play in many areas of science and technology. Examples of current inter­ est are biological and chemical pattern formation, semiconductor design, environmental problems such as solute transport in groundwater flow, phase transitions and combustion theory. Central to the theory is the equation Ut = ~cp(U) + f(u). Here ~ denotes the n-dimensional Laplacian, cp and f are given functions and the solution is defined on some domain n x [0, T] in space-time. FUn­ damental questions concern the existence, uniqueness and regularity of so­ lutions, the existence of interfaces or free boundaries, the question as to whether or not the solution can be continued for all time, the asymptotic behavior, both in time and space, and the development of singularities, for instance when the solution ceases to exist after finite time, either through extinction or through blow up.

About this title

Review:

"The book is worth reading for research workers in meteorology and geophysics, willing to deal with powerful tools of applied mathematics."
--MAP

About this edition

• Publisher: Birkhäuser
• Publication date: 1991
• ISBN 10: 0817635319
• ISBN 13: 9780817635312
• Binding: Hardcover
• Number of pages: 582
• Editor: Lloyd N.G, Ni M.G., Peletier L.A., Serrin J.