Nonlinear Diffusion Equations and Their Equilibrium States II, W.-M. Ni; L.A. Peletier; James Serrin

Автор: W.-M. Ni; L.A. Peletier; James Serrin
Название: Nonlinear Diffusion Equations and Their Equilibrium States I
ISBN: 1461396077 ISBN-13(EAN): 9781461396079
Издательство: Springer
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Описание: In recent years considerable interest has been focused on nonlinear diffu- sion problems, the archetypical equation for these being Ut = D.u + f(u).

Автор: Arnaud Debussche; Michael H?gele; Peter Imkeller
Название: The Dynamics of Nonlinear Reaction-Diffusion Equations with Small L?vy Noise
ISBN: 3319008277 ISBN-13(EAN): 9783319008271
Издательство: Springer
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Описание: Moreover the solution exhibits metastable behavior: there is a polynomial time scale along which the solution dynamics correspond asymptotically to the dynamic behavior of a finite-state Markov chain switching between the stable states.

Автор: N.G Lloyd; M.G. Ni; L.A. Peletier; J. Serrin
Название: Nonlinear Diffusion Equations and Their Equilibrium States, 3
ISBN: 1461267412 ISBN-13(EAN): 9781461267416
Издательство: Springer
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Описание: 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.