TY  - BOOK
AU  - Daskalopoulos,Panagiota
AU  - Daskalopoulos,Panagiota
AU  - Kenig,Carlos E.
TI  - Degenerate Diffusions: Initial Value Problems and Local Regularity Theory 
T2  - EMS Tracts in Mathematics (ETM)
SN  - 9783037195338
PY  - 2007///
CY  - Zuerich, Switzerland
PB  - European Mathematical Society Publishing House
KW  - Differential equations
KW  - bicssc
KW  - Partial differential equations
KW  - msc
N1  - Restricted to subscribers
N2  - The book deals with 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 = Δum, m ≥ 0, u ≥ 0. Such models arise in plasma physics, diffusions 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 is through the use of 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 ≤ mc. All of these aspects of the theory are discussed in the book.   The book is addressed to both researchers and to graduate students with a good background in analysis and some previous exposure to partial differential equations
UR  - https://doi.org/10.4171/033
UR  - http://www.ems-ph.org/img/books/daskalopoulos_mini.jpg
ER  -