Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications

, by ;
Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications by Galaktionov; Victor A., 9781584884620
Note: Supplemental materials are not guaranteed with Rental or Used book purchases.
  • ISBN: 9781584884620 | 1584884622
  • Cover: Hardcover
  • Copyright: 5/24/2004

  • Rent

    (Recommended)

    $124.76
     
    Term
    Due
    Price
    *This item is part of an exclusive publisher rental program and requires an additional convenience fee. This fee will be reflected in the shopping bag.
  • Buy New

    Usually Ships in 3-5 Business Days

    $168.13
  • eBook

    eTextBook from VitalSource Icon

    Available Instantly

    Online: 180 Days

    Downloadable: 180 Days

    *To support the delivery of the digital material to you, a digital delivery fee of $3.99 will be charged on each digital item.
    $138.60*
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.
Loading Icon

Please wait while the item is added to your bag...
Continue Shopping Button
Checkout Button
Loading Icon
Continue Shopping Button