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Causality of a Heat Conductivity System with Nonlinear Feedback from Boundary Conditions. I

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Abstract

For a distributed system described by a heat conductivity equation with nonlinear feedback from temperature to boundary conditions, a sufficient condition for the existence and causality of the operator that transforms the outer boundary action into the behavior of temperature in a closed-loop system is formulated. The norms of the operators in the sufficient condition of causality are evaluated for boundary conditions of a particular type.

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REFERENCES

  1. Solnechnyi, E.M., Causality of Operators in Problems of Mathematical Physics with Weak Nonlinearities, Diff.Uravn., 1999, vol. 35, no. 6, pp. 1–8.

    Google Scholar 

  2. Shilov, G.E., Matematicheskii analiz.Spetsial'nyi kurs (Mathematical Analysis: A Special Course), Moscow: Fizmatgiz, 1961.

    Google Scholar 

  3. Vladimirov, V.S., Obobshchennye funktsii v matematicheskoi fizike (Generalized Functions in Mathematical Physics), Moscow: Nauka, 1976.

    Google Scholar 

  4. Solnechnyi, E.M., Vyrozhdennye sistemy i ikh uspol'zovanie v zadache sinteza zadannogo povedeniya (Degenerate System and Their Application for Designing a Given Behavior), Moscow: Nauka, 1989.

    Google Scholar 

  5. Lavrent'ev, M.A. and Shabat, B.V., Metody teorii funktsii kompleksnogo peremennogo (Methods of the Theory of Functions of a Complex Variable), Moscow: Fizmatgiz, 1958.

    Google Scholar 

  6. Gantmakher, F.R., Teoriya matrits (Theory of Matrices), Moscow: Nauka, 1967. Translated under the title The Theory of Matrices, New York: Chelsea, 1959.

    Google Scholar 

  7. Samarskii, A.A. and Tikhonov, A.N., Uravneniya matematicheskoi fiziki (Equations of Mathematical Physics), Moscow: Gostekhizdat, 1953.

    Google Scholar 

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Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    E. M. Solnechnyi

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  1. E. M. Solnechnyi
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Solnechnyi, E.M. Causality of a Heat Conductivity System with Nonlinear Feedback from Boundary Conditions. I. Automation and Remote Control 63, 1388–1398 (2002). https://doi.org/10.1023/A:1020021902272

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  • DOI: https://doi.org/10.1023/A:1020021902272

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