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其他書名
Initial Value Problems and Local Regularity Theory
出版European Mathematical Society, 2007
主題Mathematics / Calculus
ISBN30371903379783037190333
URLhttp://books.google.com.hk/books?id=_UF1VkxyNhMC&hl=&source=gbs_api
EBookSAMPLE
註釋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