LEADER 02343nam 22003975a 450 001 9910151936303321 005 20091109150325.0 010 $a3-03719-533-9 024 70$a10.4171/033 035 $a(CKB)3710000000953812 035 $a(CH-001817-3)56-091109 035 $a(PPN)17815525X 035 $a(EXLCZ)993710000000953812 100 $a20091109j20070531 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDegenerate Diffusions$b[electronic resource] $eInitial Value Problems and Local Regularity Theory /$fPanagiota Daskalopoulos, Carlos E. Kenig 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2007 215 $a1 online resource (207 pages) 225 0 $aEMS Tracts in Mathematics (ETM)$v1 330 $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 = ?um, 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. 606 $aDifferential equations$2bicssc 606 $aPartial differential equations$2msc 615 07$aDifferential equations 615 07$aPartial differential equations 686 $a35-xx$2msc 700 $aDaskalopoulos$b Panagiota$0471521 702 $aKenig$b Carlos E. 801 0$bch0018173 906 $aBOOK 912 $a9910151936303321 996 $aDegenerate diffusions$9229130 997 $aUNINA