How Long to Read Higher-Order Time Asymptotics of Fast Diffusion in Euclidean Space: A Dynamical Systems Approach

How Long Does it Take to Read Higher-Order Time Asymptotics of Fast Diffusion in Euclidean Space: A Dynamical Systems Approach?

It takes the average reader 1 hour and 21 minutes to read Higher-Order Time Asymptotics of Fast Diffusion in Euclidean Space: A Dynamical Systems Approach by Jochen Denzler

Assuming a reading speed of 250 words per minute. Learn more

Description

This paper quantifies the speed of convergence and higher-order asymptotics of fast diffusion dynamics on Rn to the Barenblatt (self similar) solution. Degeneracies in the parabolicity of this equation are cured by re-expressing the dynamics on a manifold with a cylindrical end, called the cigar. The nonlinear evolution becomes differentiable in Hölder spaces on the cigar. The linearization of the dynamics is given by the Laplace-Beltrami operator plus a transport term (which can be suppressed by introducing appropriate weights into the function space norm), plus a finite-depth potential well with a universal profile. In the limiting case of the (linear) heat equation, the depth diverges, the number of eigenstates increases without bound, and the continuous spectrum recedes to infinity. The authors provide a detailed study of the linear and nonlinear problems in Hölder spaces on the cigar, including a sharp boundedness estimate for the semigroup, and use this as a tool to obtain sharp convergence results toward the Barenblatt solution, and higher order asymptotics. In finer convergence results (after modding out symmetries of the problem), a subtle interplay between convergence rates and tail behavior is revealed. The difficulties involved in choosing the right functional spaces in which to carry out the analysis can be interpreted as genuine features of the equation rather than mere annoying technicalities.

How long is Higher-Order Time Asymptotics of Fast Diffusion in Euclidean Space: A Dynamical Systems Approach?

Higher-Order Time Asymptotics of Fast Diffusion in Euclidean Space: A Dynamical Systems Approach by Jochen Denzler is 81 pages long, and a total of 20,331 words.

This makes it 27% the length of the average book. It also has 25% more words than the average book.

How Long Does it Take to Read Higher-Order Time Asymptotics of Fast Diffusion in Euclidean Space: A Dynamical Systems Approach Aloud?

The average oral reading speed is 183 words per minute. This means it takes 1 hour and 51 minutes to read Higher-Order Time Asymptotics of Fast Diffusion in Euclidean Space: A Dynamical Systems Approach aloud.

What Reading Level is Higher-Order Time Asymptotics of Fast Diffusion in Euclidean Space: A Dynamical Systems Approach?

Higher-Order Time Asymptotics of Fast Diffusion in Euclidean Space: A Dynamical Systems Approach is suitable for students ages 10 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

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