Search results for "blowup"

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Rotationally symmetric 1-harmonic flows from D2 TO S 2: Local well-posedness and finite time blowup

2010

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.

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 existenceMathematics
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A survey on algebraic dilatations

2023

In this text, we wish to provide the reader with a short guide to recent works on the theory of dilatations in Commutative Algebra and Algebraic Geometry. These works fall naturally into two categories: one emphasises foundational and theoretical aspects and the other applications to existing theories.

torsorsaffine modificationsdifferential Galois groupsformal blowupsNéron blowups[MATH] Mathematics [math]Commutative Algebra (math.AC)shtukasMathematics - Algebraic Geometryaffine blowupsFOS: Mathematicsalgebraic dilatations[MATH]Mathematics [math]Algebraic Geometry (math.AG)multi-centered dilatationsdilatations of schemesA 1 -homotopy theoryKaliman-Zaidenberg modificationslevel structuresMoy-Prasad isomorphismrepresentations of p-adic groupsMathematics - Commutative Algebramono-centered dilatationslocalizations of ringscongruent isomorphismsTannakian groupsaffine geometry
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