Degenerate Diffusions: Initial Value Problems and Local Regularity Theory: No. 1 (EMS Tracts in Mathematics) - Hardcover

Daskalopoulos, Panagiota; Kenig, Carlos E.

Hardcover

ISBN 10: 3037190337 ISBN 13: 9783037190333

Publisher: European Mathematical Society, 2007

Synopsis

The book deals with the existence, uniqueness, regularity, and asymptotic behavior of solutions to the initial value problem (Cauchy problem) and the initial-Dirichlet problem for a class of degenerate diffusions modeled on the porous medium type equation $ut = Delta um$, $m geq 0$, $u geq 0$. Such models arise in plasma physics, diffusion through porous media, thin liquid film dynamics, as well as in geometric flows such as the Ricci flow on surfaces and the Yamabe flow. The approach presented to these problems uses local regularity estimates and Harnack type inequalities, which yield compactness for families of solutions. The theory is quite complete in the slow diffusion case ($m>1$) and in the supercritical fast diffusion case ($mc < m < 1$, $mc=(n-2)+/n$) while many problems remain in the range $m leq mc$. All of these aspects of the theory are discussed in the book.

Edition details

• Publisher: European Mathematical Society
• Publication date: 2007
• Language: English
• ISBN 10: 3037190337
• ISBN 13: 9783037190333
• Binding: Hardcover
• Number of pages: 207