کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9495944 | 1335202 | 2005 | 30 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Asymptotics of the porous media equation via Sobolev inequalities
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله

چکیده انگلیسی
Let M be a compact Riemannian manifold without boundary. Consider the porous media equation uË=âµ(um), u(0)=u0âLq, âµ being the Laplace-Beltrami operator. Then, if q⩾2â¨(m-1), the associated evolution is Lq-Lâ regularizing at any time t>0 and the bound âu(t)ââ⩽C(u0)/tβ holds for t<1 for suitable explicit C(u0),γ. For large t it is shown that, for general initial data, u(t) approaches its time-independent mean with quantitative bounds on the rate of convergence. Similar bounds are valid when the manifold is not compact, but u(t) approaches uâ¡0 with different asymptotics. The case of manifolds with boundary and homogeneous Dirichlet, or Neumann, boundary conditions, is treated as well. The proof stems from a new connection between logarithmic Sobolev inequalities and the contractivity properties of the nonlinear evolutions considered, and is therefore applicable to a more abstract setting.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 225, Issue 1, 1 August 2005, Pages 33-62
Journal: Journal of Functional Analysis - Volume 225, Issue 1, 1 August 2005, Pages 33-62
نویسندگان
Matteo Bonforte, Gabriele Grillo,