Transformation operators and their applications for modeling in two-layer media

  • Authors

    • Oleg Yaremko ?????????? ??????????????? ???????????,?????, ??????
    • Natalia Yaremko Penza State University, Penza
    2014-09-02
    https://doi.org/10.14419/gjma.v2i4.3289
  • Abstract

    We present a transformation operators method which allows us to interpret piecewise-homogeneous physical processes as a perturbing of a homogeneous ones. The analytical description of mathematical models of thermal conductivity and wave processes for piecewise homogeneous media with °at symmetry is obtained by the developed in this paper transformation operators method.

    Keywords: Poisson formula, Wave equation, Heat equation, Dirichlet problem, Laplace equation.

  • References

    1. Marchenko, V. A. (2011), Sturm-Liouville operators and applications (2 ed.), Providence: American Mathematical Society.
    2. I.A. Kipriyanov, Lyakhov L.N., Raykhelgauz L.B. Singular Heat Equation with -Bessel Operator. Fundamental Solutions Journal of Mathematical Sciences V. 188, No. 3, 2013. pp. 283-293.
    3. Samko, S.G., Kilbas, A.A. and Marichev, O.I., Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, New York (1993).
    4. Carslaw, H. S.; Jaeger, J. C. , Conduction of Heat in Solids (2nd ed.), 1959,Oxford University Press,
    5. Evans, L.C. , Partial Differential Equations, American Mathematical Society,1998.
    6. R. Courant, D. Hilbert, Methods of Mathematical Physics, vol II. Interscience (Wiley) New York, 1962.
    7. Polyanin, A. D. and A. V. Manzhirov , Handbook of Mathematics for Engineers and Scientists, Chapman and Hall/CRC Press, 2007.
    8. E. Mogileva, O. Yaremko, Hermite functions with discontinuous coefficients for the solution of fractal diffusion retrospective problems, International journal of applied mathematics and informatics, Issue 3, Volume 7, 2013, p.78-86.
    9. O.E. Yaremko, Matrix integral Fourier transforms for problems with discontinuous coefficients and transformation operators, Reports Of Academy Of Sciences, Volume. 417, Issue 3, 2007, p. 323-325.
    10. Bavrin I.I., Matrosov V.L., Jaremko O. E.(2006) Operators of transformation in the analysis, mathematical physics and Pattern recog-nition. Moscow, Prometheus, p. 292.
    11. O. Yaremko, V. Selutin, N. Yaremko, The Fourier Transform with Piecewise Trigonometric Kernels and its Applications, WSEAS transactions on mathematics, Volume 13, 2014, pp. 615-625.
    12. O.E. Yaremko, Transformation operator and boundary value problems, Differential Equation. Vol.40, No. 8, 2004, pp.1149-1160.
  • Downloads

  • How to Cite

    Yaremko, O., & Yaremko, N. (2014). Transformation operators and their applications for modeling in two-layer media. Global Journal of Mathematical Analysis, 2(4), 227-234. https://doi.org/10.14419/gjma.v2i4.3289

    Received date: 2014-07-30

    Accepted date: 2014-08-30

    Published date: 2014-09-02