Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications
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A01=Victor A. Galaktionov
Author_Victor A. Galaktionov
blow-up phenomena
Category=PBKJ
cauchy
Cauchy Problem
Concavity Result
Continuous Initial Data
data
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Eventual Concavity
FBPs
geometric analysis
Global Classical Solutions
Hodograph Plane
Incomplete Extinction
initial
Interface Equation
Interface Operators
interface propagation
interfaces
Interior Gradient
Invariant Subspace
Linear Parabolic Equation
maximal
Maximal Solutions
Nonlinear Parabolic Equations
nonlinear PDE geometric intersection methods
Parabolic Equation
Parabolic PDE
Parabolic PDEs
partial differential equations
Positivity Domain
problem
proper
quasilinear
Quasilinear Parabolic Equations
Self-similar Solutions
semigroup theory
singular
Singular Interface
solutions
Stefan Problem
Sturm Theorem
TW Solution
uniqueness theorems
Product details
- ISBN 9781584884620
- Weight: 674g
- Dimensions: 156 x 234mm
- Publication Date: 24 May 2004
- Publisher: Taylor & Francis Inc
- Publication City/Country: US
- Product Form: Hardback
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Unlike the classical Sturm theorems on the zeros of solutions of second-order ODEs, Sturm's evolution zero set analysis for parabolic PDEs did not attract much attention in the 19th century, and, in fact, it was lost or forgotten for almost a century. Briefly revived by Pólya in the 1930's and rediscovered in part several times since, it was not until the 1980's that the Sturmian argument for PDEs began to penetrate into the theory of parabolic equations and was found to have several fundamental applications.
Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications focuses on geometric aspects of the intersection comparison for nonlinear models creating finite-time singularities. After introducing the original Sturm zero set results for linear parabolic equations and the basic concepts of geometric analysis, the author presents the main concepts and regularity results of the geometric intersection theory (G-theory). Here he considers the general singular equation and presents the geometric notions related to the regularity and interface propagation of solutions. In the general setting, the author describes the main aspects of the ODE-PDE duality, proves existence and nonexistence theorems, establishes uniqueness and optimal Bernstein-type estimates, and derives interface equations, including higher-order equations. The final two chapters explore some special aspects of discontinuous and continuous limit semigroups generated by singular parabolic equations.
Much of the information presented here has never before been published in book form. Readable and self-contained, this book forms a unique and outstanding reference on second-order parabolic PDEs used as models for a wide range of physical problems.
