LAUSR.org creates dashboard-style pages of related content for over 1.5 million academic articles. Sign Up to like articles & get recommendations!

Transition of blow-up mechanisms in k-equivariant harmonic map heat flow

Photo from wikipedia

In the present article, we consider blow-up phenomena appearing in k-equivariant harmonic map heat flow from to a unit sphere : Here the scalar variable u stands for latitudinal angle… Click to show full abstract

In the present article, we consider blow-up phenomena appearing in k-equivariant harmonic map heat flow from to a unit sphere : Here the scalar variable u stands for latitudinal angle on from the north pole to the south pole . The integer corresponds to the eigenvalues associated to eigenmaps , that is, harmonic maps with constant energy density. We prove constructively the existence of asymptotically non-self-similar blow-up solutions with precise description of their local space-time profiles. The blow-up solutions arise from, depending on the combination of d and k, two different approximations of the nonlinear term: either through a Dirac mass supported at the origin or via a Taylor expansion around equator map . Transition of the blow-up mechanisms arises, accordingly.

Keywords: equivariant harmonic; map; blow; harmonic map; map heat; heat flow

Journal Title: Nonlinearity
Year Published: 2020

Link to full text (if available)


Share on Social Media:                               Sign Up to like & get
recommendations!

Related content

More Information              News              Social Media              Video              Recommended



                Click one of the above tabs to view related content.