02336nam a22003495a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400150018410000390019924501470023826000820038530000340046733600260050133700260052733800360055334700240058949000390061350600660065252010570071865000350177565000400181070000310185085600320188185600730191356-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20070531sz fot ||| 0|eng d a978303719533870a10.4171/0332doi ach0018173 7aPBKJ2bicssc a35-xx2msc1 aDaskalopoulos, Panagiota,eauthor.10aDegenerate Diffusionsh[electronic resource] :bInitial Value Problems and Local Regularity Theory /cPanagiota Daskalopoulos, Carlos E. Kenig3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2007 a1 online resource (207 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v11 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe 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.07aDifferential equations2bicssc07aPartial differential equations2msc1 aKenig, Carlos E.,eauthor.40uhttps://doi.org/10.4171/033423cover imageuhttps://www.ems-ph.org/img/books/daskalopoulos_mini.jpg