Advertisement

Inverse Problems of Determination of the Right-Hand Side Term in the Degenerate Higher-Order Parabolic Equation on a Plane

  • Vitaly L. Kamynin
  • Tatiana I. BukharovaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10187)

Abstract

We establish existence and uniqueness theorems as well as the theorem on stability under perturbations of the input data for the solution of the inverse problem for a degenerate higher-order parabolic equation on a plane with integral observation. We also obtain the estimates of the solution with constants explicitly written out in terms of the input data of the problem.

References

  1. 1.
    Kamynin, V.L.: On the solvability of the inverse problem for determining the right-hand side of a degenerate parabolic equation with integral observation. Math. Notes 98(5), 765–777 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Ivanchov, M., Saldina, N.: An inverse problem for strongly degenerate heat equation. J. Inverse Ill-Posed Prob. 14(5), 465–480 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Cannarsa, P., Tort, J., Yamamoto, M.: Determination of source terms in degenerate parabolic equation. Inverse Prob. 26(10), 105003 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Deng, Z.C., Qian, K., Rao, X.B., Yang, L.: An inverse problem of identifying the source coefficient in degenerate heat equation. Inverse Prob. Sci. Eng. 23(3), 498–517 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Huzyk, N.: Inverse problem of determining the coefficients in degenerate parabolic equation. Electron. J. Differ. Equ. 172, 1–11 (2014)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Kawamoto, A.: Inverse problems for linear degenerate parabolic equations by “time-like” Carleman estimate. J. Inverse Ill-posed Prob. 23(1), 1–21 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Bouchouev, I., Isakov, V.: Uniqueness, stability and numerical methods for the inverse problem that arises in financial markets. Inverse Prob. 15(3), 95–116 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Lishang, J., Yourshan, T.: Identifying the volatibility of underlying assets from option prices. Inverse Prob. 17(1), 137–155 (2001)CrossRefzbMATHGoogle Scholar
  9. 9.
    Lishang, J., Qihong, C., Lijun, W., Zhang, J.E.: A new well-posed algorithm to recover implied local volatibility. Quant. Finance 3(6), 451–457 (2003)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Prilepko, A.I., Orlovskii, D.G.: Determination of the parameter of an evolution equation and inverse problems of mathematical physics I. Differ. Equ. 21(1), 96–104 (1985)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Prilepko, A.I., Orlovskii, D.G.: Determination of the parameter of an evolution equation and inverse problems of mathematical physics II. Differ. Equ. 21(4), 472–477 (1985)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Kamynin, V.L., Francini, E.: An inverse problem for a higher-order parabolic equation. Math. Notes 64(5–6), 590–599 (1999)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Kruzhkov, S.N.: Quasilinear parabolic equations and systems with two independent variables. Trudy Sem. im. I.G.Petrovskogo 5, 217–272 (1979)MathSciNetGoogle Scholar
  14. 14.
    Besov, O.V., Il’in, V.P., Nikolskii, S.M.: Integral’nye predstavleniya funkcii i teoremy vlozheniya (Integral reprezentation of functions and embedding theorems). Nauka, Moscow (1975)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)MoscowRussia

Personalised recommendations