6533b853fe1ef96bd12ac133
RESEARCH PRODUCT
Rotationally symmetric 1-harmonic flows from D2 TO S 2: Local well-posedness and finite time blowup
Salvador MollLorenzo Giacomellisubject
Well-posed problemDirichlet problemApplied MathematicsMathematical analysisMathematics::Analysis of PDEsRotational symmetryMixed boundary conditionrotational symmetryferromagnetism; blowup; 1-harmonic flow; image processing; local existence; dirichlet problem; partial differential equations; rotational symmetryferromagnetism1-harmonic flowblowupimage processingComputational Mathematicssymbols.namesakeFlow (mathematics)Dirichlet boundary conditionsymbolspartial differential equationsInitial value problemBoundary value problemdirichlet problemAnalysislocal existenceMathematicsdescription
The 1-harmonic flow from the disk to the sphere with constant Dirichlet boundary conditions is analyzed in the case of rotational symmetry. Sufficient conditions on the initial datum are given, such that a unique classical solution exists for short times. Also, a sharp criterion on the boundary condition is identified, such that any classical solution will blow up in finite time. Finally, nongeneric examples of finite time blowup are exhibited for any boundary condition.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2010-01-01 |