Sharp energy estimates for nonlinear fractional diffusion equations
نویسندگان
چکیده
منابع مشابه
Sharp Energy Estimates for Nonlinear Fractional Diffusion Equations
We study the nonlinear fractional equation (−∆)u = f(u) in R, for all fractions 0 < s < 1 and all nonlinearities f . For every fractional power s ∈ (0, 1), we obtain sharp energy estimates for bounded global minimizers and for bounded monotone solutions. They are sharp since they are optimal for solutions depending only on one Euclidian variable. As a consequence, we deduce the one-dimensional ...
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We establish quantitative estimates for solutions u(t, x) to the fractional nonlinear diffusion equation, ∂tu + (−∆)(u) = 0 in the whole range of exponents m > 0, 0 < s < 1. The equation is posed in the whole space x ∈ R. We first obtain weighted global integral estimates that allow to establish existence of solutions for classes of large data. In the core of the paper we obtain quantitative po...
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ژورنال
عنوان ژورنال: Calculus of Variations and Partial Differential Equations
سال: 2012
ISSN: 0944-2669,1432-0835
DOI: 10.1007/s00526-012-0580-6