scientific article; zbMATH DE number 778934

zbMath0926.35023MaRDI QIDQ4842022

Juan J. L. Velazquez

Publication date: 15 November 1999

Full work available at URL: http://www.numdam.org/item?id=ASNSP_1994_4_21_4_595_0

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zbMATH Keywords

generalized solutionssingularitiesfast and slow blow up

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10)

Related Items (14)

Blow up dynamics for the hyperbolic vanishing mean curvature flow of surfaces asymptotic to the Simons cone ⋮ Ancient asymptotically cylindrical flows and applications ⋮ Liouville theorems and blow up behaviour in semilinear reaction diffusion systems ⋮ Existence of mean curvature flow singularities with bounded mean curvature ⋮ Generic mean curvature flow. I: Generic singularities ⋮ Curvature Blow-up in Doubly-warped Product Metrics Evolving by Ricci Flow ⋮ Formation of singularities in nonlinear dispersive PDEs ⋮ Entropy and generic mean curvature flow in curved ambient spaces ⋮ Analysis of Velázquez’s solution to the mean curvature flow with a type II singularity ⋮ Refined construction of type II blow-up solutions for semilinear heat equations with Joseph-Lundgren supercritical nonlinearity ⋮ Singularity patterns in a chemotaxis model ⋮ A nonlinear Fokker-Planck equation modelling the approach to thermal equilibrium in a homogeneous plasma ⋮ Blow-up dynamics for the hyperbolic vanishing mean curvature flow of surfaces asymptotic to a Simons cone ⋮ A local singularity analysis for the Ricci flow and its applications to Ricci flows with bounded scalar curvature

Cites Work

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• On the blowup of multidimensional semilinear heat equations
• Motion of level sets by mean curvature. I
• On the formation of singularities in the curve shortening flow
• Asymptotic behavior for singularities of the mean curvature flow
• The existence of bounded solutions of a semilinear elliptic equation
• The heat equation shrinking convex plane curves
• The heat equation shrinks embedded plane curves to round points
• Parabolic equations for curves on surfaces. II: Intersections, blow-up and generalized solutions
• Parabolic equations for curves on surfaces. I: Curves with \(p\)-integrable curvature
• Stable blow-up patterns
• Flat blow-up in one-dimensional semilinear heat equations
• Shortening space curves and flow through singularities
• Motion of a set by the curvature of its boundary
• Asymptotic shape of cusp singularities in curve shortening
• Blow-up behaviour of one-dimensional semilinear parabolic equations
• Minimal varieties in Riemannian manifolds
• Minimal cones and the Bernstein problem
• Nondegeneracy of blowup for semilinear heat equations
• Asymptotically self‐similar blow‐up of semilinear heat equations
• The Existence of Bounded Solutions of a Semilinear Heat Equation
• Blow–Up Profiles in One–Dimensional. Semilinear Parabolic Problems
• Higher Dimensional Blow Up for Semilinear Parabolic Equations
• Refined asymptotics for the blowup of u_t — δu = u^p
• Phase transitions and generalized motion by mean curvature
• The Motion of a Surface by Its Mean Curvature. (MN-20)
• Classification of Singularities for Blowing up Solutions in Higher Dimensions
• Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations

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