
Degenerate diffusions : : Initial value problems and local regularity theory / Panagiota Daskalopoulos, Carlos E. Kenig
Tác giả : Panagiota Daskalopoulos, Carlos E. Kenig
Nhà xuất bản : European Mathematical Society
Năm xuất bản : 2007
Nơi xuất bản : Germany
Mô tả vật lý : 195 p. ; 25 cm
ISBN : 3037190333
Số phân loại : 515.353
Tùng thư :
Tracts in mathematics 1
Chủ đề : 1. Những vấn đề của giá trị giới hạn. 2. Boundary value problems. 3. Toán học.
Thông tin chi tiết
Tóm tắt : | 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 $u_t = \Delta u^m$, $m \geq 0$, $u \geq 0$. 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 ($m>1$) and in the supercritical fast diffusion case ($m_c < m < 1$, $m_c=(n-2)_+/n$) while many problems remain in the range $m \leq m_c$. All of these aspects of the theory are discussed in the book. |
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https://lrcopac.ctu.edu.vn/pages/opac/wpid-detailbib-id-134073.html |