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A Stability Technique for Evolution Partial Differential Equations: A Dynamical Systems Approach

✍ Scribed by Victor A. Galaktionov, Juan Luis Vázquez

Publisher
Birkhäuser
Year
2004
Tongue
English
Leaves
386
Series
Progress in nonlinear differential equations and their applications 56
Edition
Softcover reprint of the original 1st ed. 2004
Category
Library
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✦ Synopsis

* Introduces a state-of-the-art method for the study of the asymptotic behavior of solutions to evolution partial differential equations.

* Written by established mathematicians at the forefront of their field, this blend of delicate analysis and broad application is ideal for a course or seminar in asymptotic analysis and nonlinear PDEs.

* Well-organized text with detailed index and bibliography, suitable as a course text or reference volume.

✦ Table of Contents

Front Matter....Pages i-xix
Stability Theorem: A Dynamical Systems Approach....Pages 1-12
Nonlinear Heat Equations: Basic Models and Mathematical Techniques....Pages 13-55
Equation of Superslow Diffusion....Pages 57-79
Quasilinear Heat Equations with Absorption. The Critical Exponent....Pages 81-125
Porous Medium Equation with Critical Strong Absorption....Pages 127-167
The Fast Diffusion Equation with Critical Exponent....Pages 169-187
The Porous Medium Equation in an Exterior Domain....Pages 189-215
Blow-up Free-Boundary Patterns for the Navier-Stokes Equations....Pages 217-236
Equation u t = u xx + u ln 2 u: Regional Blow-up....Pages 237-263
Blow-up in Quasilinear Heat Equations Described by Hamilton—Jacobi Equations....Pages 265-298
A Fully Nonlinear Equation from Detonation Theory....Pages 299-325
Further Applications to Second- and Higher-Order Equations....Pages 327-357
Back Matter....Pages 359-377

✦ Subjects

Differential equations, Partial;Differential equations, Parabolic;Differentiable dynamical systems;Stability;Équations aux dérivées partielles;Équations différentielles paraboliques;Dynamique différentiable;Stabilité;Stabilité;Partielle Differentialgleichung -- Stabilität;Parabolische Differentialgleichung -- Stabilität;Differenzierbares dynamisches System -- Stabilität

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