Skip to main content
SpringerLink
Log in

The problem of recovering the temperature and moisture fields in a porous body from incomplete initial data

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

We propose a statement and computational scheme for the inverse problem of recovering the temperature field and the moisture distribution in a body with incompletely known initial conditions. We give additional relations on the integral values of the unknown functions and introduce a test for the choice of a unique solution of the problem from the set of admissible temperature and moisture functions. We state conditions for independence of the additional data and obtain systems of equations and conditions that close the initial indeterminate problem. We study in detail the example of heat-moisture conduction in a layer.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature Cited

  1. B. V. Gera, “Mathematical modeling in the problem of determining the temperature field and the moisture distribution in a body from incomplete data”, in:Signal and Image Processing and Pattern Recognition: Proceedings of the First All-Ukrainian Conference [in Ukrainian], Kiev (1992), pp. 172–174.

  2. B. V. Gera, “Optimal recovery of the initial temperature distribution of a body from the data of measurement of the temperature characteristics at later times”, in:Questions of Optimal Computations: Proceedings of a Symposium [in Ukrainian], Kiev (1993), pp. 45–46.

  3. B. V. Gera, “Optimizing the estimates of initial conditions in heat-conduction problems”, Preprint Nats. Akad. Nauk Ukr. Tsentr Mat. Mod., No. 8-95, L'viv (1995).

  4. J. L. Lions, “Remarks on systems with incomplete data”, in:Variational Methods in Geosciences: Proceedings of the International Symposium in Norman, OK, Oct. 15–17, 1985, Elsevier, Amsterdam (1986), pp. 145–159.

    Google Scholar 

  5. H. R. Thomas, “Modelling two-dimensional heat and moisture transfer in unsaturated soils, including gravity effects”,Int. J. for Numerical and Analytical Methods in Geomechanics,9, No. 6, 573–588 (1985).

    MATH  Google Scholar 

Download references

Authors
  1. B. V. Gera
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated fromMatematichni Metodi ta Fiziko-mekhanichni Polya, Vol. 39, No. 1, 1996, pp. 66–73.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gera, B.V. The problem of recovering the temperature and moisture fields in a porous body from incomplete initial data. J Math Sci 86, 2578–2584 (1997). https://doi.org/10.1007/BF02356100

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02356100

Keywords

Search

Navigation