02343nam 22003975a 450 991015193630332120091109150325.03-03719-533-910.4171/033(CKB)3710000000953812(CH-001817-3)56-091109(PPN)17815525X(EXLCZ)99371000000095381220091109j20070531 fy 0engurnn|mmmmamaatxtrdacontentcrdamediacrrdacarrierDegenerate Diffusions[electronic resource] Initial Value Problems and Local Regularity Theory /Panagiota Daskalopoulos, Carlos E. KenigZuerich, Switzerland European Mathematical Society Publishing House20071 online resource (207 pages)EMS Tracts in Mathematics (ETM)1The 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.Differential equationsbicsscPartial differential equationsmscDifferential equationsPartial differential equations35-xxmscDaskalopoulos Panagiota471521Kenig Carlos E.ch0018173BOOK9910151936303321Degenerate diffusions229130UNINA