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Well-Posed Problems

  • Reference work entry
Encyclopedia of Thermal Stresses

Synonyms

Continuous dependence; Existence; Lagrange identity method; Linear thermoelasticity; Logarithmic convexity method; Uniqueness; Well-posedness

Overview

The mathematical model of the linear thermoelasticity is understood to be well posed in the sense of Hadamard if the corresponding boundary–initial value problem possesses a unique solution that depends continuously on the prescribed data. This definition is made precise by indicating the space to which the solution must belong and the measure in which continuous dependence is desired. A problem is called improperly posed (or ill posed) if it fails to have a global solution, if it fails to have a unique solution, or if the solution does not depend continuously on the data.

Uniqueness is equivalent to proving that at most only the trivial exists for homogeneous given data. Energy arguments are among the most frequently used methods to establish uniqueness in linear thermoelastodynamics (see, e.g., Weiner [1], Ionescu-Cazimir [2, 3...

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Author information

Authors and Affiliations

  1. Department of Mathematics, Alexandru Ioan Cuza University of Iaşi, Blvd. Carol I, no. 11, 700506, Iaşi, Romania

    Stan Chiriţă

  2. Octav Mayer Institute of Mathematics, Romanian Academy, Blvd. Carol I, nr. 8, 700505, Iaşi, Romania

    Stan Chiriţă

Authors
  1. Stan Chiriţă
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Corresponding author

Correspondence to Stan Chiriţă .

Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, Rochester Institute of Technology, Rochester, NY, USA

    Richard B. Hetnarski

  2. Naples, FL, USA

    Richard B. Hetnarski

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Chiriţă, S. (2014). Well-Posed Problems. In: Hetnarski, R.B. (eds) Encyclopedia of Thermal Stresses. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2739-7_264

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