Optimal control problems for an extensible beam equation

DOI10.1016/j.jmaa.2008.12.020zbMath1170.35020OpenAlexW2043729594MaRDI QIDQ1014707

Jin-Soo Hwang

Publication date: 29 April 2009

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2008.12.020

zbMATH Keywords

necessary optimality conditionsclamped boundary conditionsGâteaux differentiability

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Control/observation systems governed by partial differential equations (93C20) Initial-boundary value problems for higher-order hyperbolic equations (35L35) Higher-order nonlinear hyperbolic equations (35L75)

Related Items (11)

Optimal control problems for a von Kármán system with long memory ⋮ Parameter identification problems for an extensible beam equation ⋮ Optimal control problem for a viscoelastic beam and its Galerkin approximation ⋮ Fréchet differentiability for an extensible beam equation and its application to bilinear minimax control problems ⋮ Minimax optimal control problems for an extensible beam equation with uncertain initial velocity ⋮ A Kirchhoff type equation in a nonlinear model of shell vibration ⋮ Optimal control problem with necessary optimality conditions for the viscous Dullin-Gottwald-Holm equation ⋮ Fréchet differentiability for a damped Kirchhoff-type equation and its application to bilinear minimax optimal control problems ⋮ Quadratic cost minimax optimal control problems for a semilinear viscoelastic equation with long memory ⋮ Pareto optimal control problem and its Galerkin approximation for a nonlinear one-dimensional extensible beam equation ⋮ Optimal control problems for an extensible beam equation with pointwise state constraints

Cites Work

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• On semi-linear second order Volterra integro-differential equations in Hilbert space
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• On a new class of nonlinear wave equations
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• Optimal control problems for the equation of motion of membrane with strong viscosity
• Stability theory for an extensible beam
• Decay estimates for the generalized damped extensible string and beam equations
• The Cauchy problem for Kirchhoff equations
• Equivalent Norms for Sobolev Spaces
• Infinite Systems of Nonlinear Oscillation Equations with Linear Damping

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