Optimality of piecewise thermal conductivity  in a snow-ice thermodynamic system

Wei  Lv; Ruirui Sui

doi:10.3934/naco.2015.5.47

Article Contents

2015, Volume 5, Issue 1: 47-57. Doi: 10.3934/naco.2015.5.47

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Optimality of piecewise thermal conductivity in a snow-ice thermodynamic system

Wei Lv^1, and
Ruirui Sui^1,

1.
Department of Mathematics, Shanghai University, Shanghai 200444

Received: December 2014

Revised: March 2015

Published: February 2015

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Abstract

This article is intended to provide the optimality of piecewise thermal conductivity in a snow-ice thermodynamic system. Based on the temperature distribution characteristics of snow and sea ice, we construct a piecewise smooth thermodynamic system coupled by snow and sea ice. Taking the piecewise thermal conductivities of snow and sea ice as control variables and the temperature deviations obtained from the system and the observations as the performance criterion, an identification model with state constraints is given. The dependency relationship between state and control variables is proven, and the existence of the optimal control is discussed. The work can provide a theoretical foundation for simulating temperature distributions of snow and sea ice.

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Mathematics Subject Classification: Primary: 49J20; Secondary: 35K05.

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