Behavior of the gradient for solutions of parabolic equations on the circle

DOI10.1007/s00526-004-0298-1zbMath1163.35403OpenAlexW1970574944MaRDI QIDQ2583042

Dong-Ho Tsai

Publication date: 13 January 2006

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-004-0298-1

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Initial value problems for second-order parabolic equations (35K15)

Related Items (8)

A unified flow approach to smooth, even \(L_p\)-Minkowski problems ⋮ Deforming a hypersurface by Gauss curvature and support function ⋮ Aleksandrov reflection for extrinsic geometric flows of Euclidean hypersurfaces ⋮ On a simple maximum principle technique applied to equations on the circle ⋮ Using Aleksandrov reflection to estimate the location of the center of expansion ⋮ Expanding convex immersed closed plane curves ⋮ Evolving a convex closed curve to another one via a length-preserving linear flow ⋮ Contracting convex immersed closed plane curves with slow speed of curvature

Cites Work

• Unnamed Item
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• Convergence, asymptotic periodicity, and finite-point blow-up in one- dimensional semilinear heat equations
• Geometric expansion of convex plane curves
• On the formation of singularities in the curve shortening flow
• The heat equation shrinking convex plane curves
• Symmetry and related properties via the maximum principle
• An expansion of convex hypersurfaces
• Evolving convex curves
• Geometric aspects of Aleksandrov reflection and gradient estimates for parabolic equations
• Aleksandrov reflection and nonlinear evolution equations. I: The \(n\)-sphere and \(n\)-ball
• The zero set of a solution of a parabolic equation.

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