General Parabolic Mixed Order Systems in Lp and Applications: 239 (Operator Theory: Advances and Applications)

Book Details

• Author: Robert Denk

• Brand: Birkhauser

• Edition: 2013 ed.

• Binding: Hardcover

• Number of Pages: 250

• Release Date: 10-12-2013

• ISBN: 9783319019994

• Package Dimensions: 9.5 x 6.4 x 0.7 inches

• Languages: English

About the Book

In Robert Denk’s groundbreaking work, "A Theory for General Linear Parabolic Partial Differential Equations", readers are presented with a sophisticated approach to understanding linear parabolic partial differential equations. The book introduces a theory that deals with both equations with inhomogeneous symbol structures and mixed-order systems, with a focus on practical applications.

This comprehensive study covers essential topics such as the Stokes system, free boundary value problems, and nonlinear problems. By using the concept of the Newton polygon, Denk's theory goes beyond standard methods like semigroup theory, offering readers a powerful toolkit to tackle even the most complex equations.

Key concepts such as well-posedness in Lp-Lq-Sobolev spaces—the heart of the theory—are explored in great detail, providing insights into the maximal regularity required for solving nonlinear problems. Additionally, the book expands to various non-integer Lp-Sobolev spaces, including Besov spaces, Bessel potential spaces, and Triebel–Lizorkin spaces, offering new perspectives for dealing with complex differential equations.

The book also provides a selection of practical applications that demonstrate how these theoretical advancements can be applied in real-world scenarios, such as solving the generalized thermoelastic plate equation and the two-phase Navier-Stokes equations.

For advanced readers in the field of mathematics, physics, or engineering, this book serves as an essential reference, presenting a deep theoretical understanding while remaining rooted in real-world applications.