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On the evolution operators for some equations of mathematical physics with variable coefficients

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Abstract

It is shown that, with the help of a relatively simple operator technique, it is possible to solve, from a common point of view, the Cauchy problem for many important equations of mathematical physics with variable coefficients. This result is applied to the equations of kinetic theory, and diffusion and heat conduction equations. We discuss the problem of equivalence of different schemes of expansion according to the Hausdorff formula.

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References

  1. L. Hörmander,Analysis of Linear Partial Differential Operators [Russian translation], Nauka, Moscow (1986).

    Google Scholar 

  2. L. D. Landau, E. M. Lifshits, and L. P. Pitaevskii,Physical Kinetics [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  3. V. I. Fushchich, V. M. Shtelen', and N. I. Serov,Symmetry Analysis and Exact Solutions of Nonlinear Equations of Mathematical Physics [in Russian], Naukova Dumka, Kiev (1989).

    Google Scholar 

  4. W. Magnus, “On the exponential solution of differential equations for linear operators,”Commun. Pure Appl. Math.,7, 649–673 (1954).

    Google Scholar 

  5. R. M. Wilcox, “Exponential operators and parameter differentiation in quantum physics,”J. Math. Phys., No. 4, 962–982 (1967).

    Google Scholar 

  6. D. P. Zhelobenko and A. I. Shtern,Representations of Lie Groups [in Russian], Nauka, Moscow (1983).

    Google Scholar 

  7. J. M. Ziman,Elements of Advanced Quantum Theory [Russian translation], Mir, Moscow (1971).

    Google Scholar 

  8. R. Kubo,Statistical Mechanics [Russian translation], Mir, Moscow (1967).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Fundamental Problems of Technology, Polish Academy of Sciences, Warsaw

    S. Kochmanski

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  1. S. Kochmanski
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 7, pp. 857–869, July, 1994.

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Kochmanski, S. On the evolution operators for some equations of mathematical physics with variable coefficients. Ukr Math J 46, 938–952 (1994). https://doi.org/10.1007/BF01056671

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  • DOI: https://doi.org/10.1007/BF01056671

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