01590nam a2200217Ia 4500 CTU_134073 210402s9999 xx 000 0 und d 2216000 515.353 D229 Daskalopoulos, Panagiota Degenerate diffusions : Initial value problems and local regularity theory Panagiota Daskalopoulos, Carlos E. Kenig Germany European Mathematical Society 2007 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 _t = \Delta u^m \geq 0 \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 ( >1 and in the supercritical fast diffusion case ( _c < m < 1 _c=(n-2)_+/n while many problems remain in the range \leq m_c All of these aspects of the theory are discussed in the book. Boundary value problems,Những vấn đề của giá trị giới hạn Trọng Hải Trung tâm Học liệu Trường Đại học Cần Thơ