An extremal eigenvalue problem arising in heat conduction

DOI10.1016/J.MATPUR.2016.02.005zbMath1339.49036OpenAlexW2292090683MaRDI QIDQ280829

Gregoire Nadin, Yannick Privat

Publication date: 10 May 2016

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2016.02.005

zbMATH Keywords

heat conductioncalculus of variationextremal eigenvalue problemlateral surface constraintLebesgue density theoremoptimal shapesSturm-Liouville eigenvalue

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Existence theories for optimal control problems involving ordinary differential equations (49J15) Optimization of shapes other than minimal surfaces (49Q10) Optimality conditions for problems involving ordinary differential equations (49K15) Asymptotic expansions of solutions to ordinary differential equations (34E05) Variational methods for eigenvalues of operators (49R05)

Cites Work

• Functional analysis, Sobolev spaces and partial differential equations
• The optimal shape of a dendrite sealed at both ends
• Elliptic partial differential equations of second order
• On spectral theory of elliptic operators
• Shape minimization of dendritic attenuation
• Optimal shape profiles for cooling fins of high and low conductivity
• What Is the Optimal Shape of a Fin for One-Dimensional Heat Conduction?
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