Global existence of classical solutions to the minimal surface equation with slow decay initial value

DOI10.1016/J.AMC.2010.01.079zbMath1184.49042OpenAlexW1985704677MaRDI QIDQ963943

Yu-Zhu Wang, Yin-Xia Wang

Publication date: 14 April 2010

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2010.01.079

zbMATH Keywords

Cauchy problemminimal surface equationglobal existenceclassical solutions

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Existence theories for optimal control problems involving partial differential equations (49J20)

Related Items (6)

GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO CAHN–HILLIARD EQUATION WITH INERTIAL TERM ⋮ Asymptotic behavior of solutions to the damped nonlinear hyperbolic equation ⋮ Global existence and asymptotic behavior of solutions for a semi-linear wave equation ⋮ Global existence of timelike minimal surface of general co-dimension in Minkowski space time ⋮ Triply periodic minimal surface using a modified Allen-Cahn equation ⋮ Global existence and asymptotic behavior of solutions to a nonlinear wave equation of fourth-order

Cites Work

• Lectures on nonlinear hyperbolic differential equations
• Equations for the motion of relativistic torus in the Minkowski space R1+n
• Uniform decay estimates and the lorentz invariance of the classical wave equation
• Global existence for nonlinear wave equations
• Remarks on the global sobolev inequalities in the minkowski space Rⁿ⁺¹
• A remark on global existence for small initial data of the minimal surface equation in Minkowskian space time
• Life-span of classical solutions to fully nonlinear wave equations—II
• Hypersurfaces in Minkowski space with vanishing mean curvature
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