|کد مقاله||کد نشریه||سال انتشار||مقاله انگلیسی||ترجمه فارسی||نسخه تمام متن|
|6425044||1633783||2017||66 صفحه PDF||سفارش دهید||دانلود رایگان|
We study the uniqueness, existence, and properties of bounded distributional solutions of the initial value problem for the anomalous diffusion equation âtuâLÎ¼[Ï(u)]=0. Here LÎ¼ can be any nonlocal symmetric degenerate elliptic operator including the fractional Laplacian and numerical discretizations of this operator. The function Ï:RâR is only assumed to be continuous and nondecreasing. The class of equations include nonlocal (generalized) porous medium equations, fast diffusion equations, and Stefan problems. In addition to very general uniqueness and existence results, we obtain stability, L1-contraction, and a priori estimates. We also study local limits, continuous dependence, and properties and convergence of a numerical approximation of our equations.
Journal: Advances in Mathematics - Volume 305, 10 January 2017, Pages 78-143