Dewey Class 
515.353 
Title 
Nonlinear Diffusion Equations and Their Equilibrium States, 3 ([EBook] :) : Proceedings from a Conference held August 20–29, 1989 in Gregynog, Wales / / edited by N. G. Lloyd, W. M. Ni, L. A. Peletier, J. Serrin. 
Added Personal Name 
Lloyd, N. G. editor. 
Ni, W. M. editor. 
Peletier, L. A. editor. 
Serrin, J. editor. 
Other name(s) 
SpringerLink (Online service) 
Publication 
Boston, MA : : Birkhäuser Boston : : Imprint: Birkhäuser, , 1992. 
Physical Details 
X, 572 p. : online resource. 
Series 
Progress in nonlinear differential equations and their applications ; 7 
ISBN 
9781461203933 
Summary Note 
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 ndimensional Laplacian, cp and f are given functions and the solution is defined on some domain n x [0, T] in spacetime. 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.: 
Contents note 
Blow up in Rn for a Parabolic Equation with a Damping Nonlinear Gradient Term  Shrinking Doughnuts  Higher Approximations to Eigenvalues for a Nonlinear Elliptic Problem  Positive Solutions of Emden Equations in ConeLike Domains  Nonlinear Parabolic Equations Arising in Semiconductor and Viscous Droplets Models  A Parabolic Equation with a MeanCurvature Type Operator  Heat Flows and Relaxed Energies for Harmonic Maps  Local Existence and Uniqueness of Positive Solutions of the Equation ?u + (1 + ??(r))u(n+2)/(n2) = 0, in Rn and a Related Equation  Singularities of Solutions of a Class of Quasilinear Equations in Divergence Form  An Existence Result Via LsRegularity for Some Nonlinear Elliptic Equations  Identifying a TimeDependent Unknown Coefficient in a Nonlinear Heat Equation  On the Structure of Solutions for Some Semilinear Elliptic Equations  A Note on Boundary Regularity for Certain Degenerate Parabolic Equations  The Quenching Problem on the N dimensional Ball  Global Solutions for a Class of MongeAmpère Equations  The Structure of Solutions near an Extinction Point in a Semilinear Heat Equation with Strong Absorption: A Formal Approach  On a Conjecture by Hagan and Brenner  A Nonlinear DiffusionAbsorption Equation with Unbounded Initial Data  A Free Boundary Problem Arising in Plasma Physics  Remarks on Quenching, Blow Up and Dead Cores  Bifurcation at Boundary Points of the Continuous Spectrum  A Comparison Result and Elliptic Equations Involving Subcritical Exponents  Advances in Quenching  On Some Almost Everywhere Symmetry Theorems  Symmetry Properties of Finite Total Mass Solutions of Matukuma Equation  An Exact Reduction of Maxwell’ s Equations  A General ITheorem for Semilinear Elliptic Equations  On Supercritical Phenomena  On the Existence and Shape of Solutions to a Semilinear Neumann Problem  Global Asymptotic Stability for Strongly Nonlinear Second Order Systems  The Existence and Asymptotic Behaviour of Similarity Solutions to a Quasilinear Parabolic Equation  Maximal Solutions of Singular Diffusion Equations with General Initial Data  The Evolution of Harmonic Maps: Existence, Partial Regularity, and Singularities  Two Dimensional EmdenFowler Equation with Exponential Nonlinearity  Global Bifurcation of Positive Solutions in Rn  Conformai Asymptotics of the Isothermal Gas Spheres Equation  Chemical Interfacial Reaction Models with Radial Symmetry. 
System details note 
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users) 
Internet Site 
http://dx.doi.org/10.1007/9781461203933 
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