Heat flow for Dirichlet-to-Neumann operator with critical growth

DOI10.1016/j.aim.2018.01.010zbMath1391.35199OpenAlexW2792951612MaRDI QIDQ1705460

Fei Fang, Zhong Tan

Publication date: 15 March 2018

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2018.01.010

zbMATH Keywords

blowupglobal solutionscritical growthDirichlet-to-Neumann operatorconcentration phenomenon

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Critical exponents in context of PDEs (35B33)

Related Items (4)

The global solution and blowup of a spatiotemporal EIT problem with a dynamical boundary condition ⋮ Global existence and finite time blow-up of solutions for a class of Dirichlet-to-Neumann operator heat flow equations with critical growth ⋮ Global existence and blowup of solutions to semilinear fractional reaction-diffusion equation with singular potential ⋮ Nonlinear elliptic-parabolic problem involving p-Dirichlet-to-Neumann operator with critical exponent

Cites Work

• Unnamed Item
• \(G\)-convergence, Dirichlet to Neumann maps and invisibility
• The Brezis-Nirenberg type problem involving the square root of the Laplacian
• The Dirichlet-to-Neumann operator on rough domains
• The Nehari manifold for elliptic equation involving the square root of the Laplacian
• Dirichlet-to-Neumann semigroup acts as a magnifying glass
• A global compactness result for elliptic boundary value problems involving limiting nonlinearities
• Generalized \(Q\)-functions and Dirichlet-to-Neumann maps for elliptic differential operators
• The concentration-compactness principle in the calculus of variations. The limit case. II
• Positive solutions of nonlinear problems involving the square root of the Laplacian
• Boundedness of global solutions of nonlinear diffusion equations
• Conformal deformation of a Riemannian metric to a scalar flat metric with constant mean curvature on the boundary
• Saddle points and instability of nonlinear hyperbolic equations
• Asymptotic stability and blowing up of solutions of some nonlinear equations
• Remarks on the Schrödinger operator with singular complex potentials
• Energy identity of harmonic map flows from surfaces at finite singular time
• On singularities of the heat flow for harmonic maps from surfaces into spheres
• On partial regularity of the borderline solution of semilinear parabolic equation with critical growth
• Asymptotic expansion of the trace of the heat kernel associated to the Dirichlet-to-Neumann operator
• Conformal deformations to scalar-flat metrics with constant mean curvature on the boundary
• GLOBAL SOLUTION AND BLOWUP OF SEMILINEAR HEAT EQUATION WITH CRITICAL SOBOLEV EXPONENT
• The Dirichlet to Neumann operator for elliptic complexes
• Solutions globales d'equations de la chaleur semi lineaires.
• Existence results for the Yamabe problem on manifolds with boundary
• Electrical impedance tomography and Calderón's problem
• Bubbling of the heat flows for harmonic maps from surfaces
• Inverse problems: seeing the unseen
• An Extension Problem Related to the Fractional Laplacian

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