Inverse Boundary Value Problem for Non-linear Hyperbolic Partial Differential Equations

Preprint English OPEN
Nakamura, Gen; Vashisth, Manmohan;
(2017)
  • Subject: Mathematics - Analysis of PDEs

In this article we are concerned with an inverse boundary value problem for a non-linear wave equation of divergence form with space dimension $n\geq 3$. In particular the so called the interior determination problem. This non-linear wave equation has a trivial solution... View more
  • References (23)
    23 references, page 1 of 3

    [1] Belishev, Mikhail I. Boundary control in reconstruction of manifolds and metrics (the BC method). Inverse Problems 13 (1997), no. 5, R1R45.

    [2] Choulli, Mourad; Ouhabaz, El Maati; Yamamoto, Masahiro. Stable determination of a semilinear term in a parabolic equation. Commun. Pure Appl. Anal. 5 (2006), no. 3, 447462.

    [3] Denisov, Alexander M. An inverse problem for a quasilinear wave equation. (Russian) Di er. Uravn. 43 (2007), no. 8, 1097{1105, 1151{1152; translation in Di er. Equ. 43 (2007), no. 8, 11231131.

    [4] Grasselli, Maurizio. Local existence and uniqueness for a quasilinear hyperbolic inverse problem. Appl. Anal. 32 (1989), no. 1, 1530.

    [5] Hervas, David; Sun, Ziqi. An inverse boundary value problem for quasilinear elliptic equations. (English summary) Comm. Partial Di erential Equations 27 (2002), no. 11-12, 24492490.

    [6] Isakov, Victor. Uniqueness of recovery of some systems of quasilinear elliptic and parabolic partial di erential equations. Nonlinear problems in mathematical physics and related topics, II, 201212, Int. Math. Ser. (N. Y.), 2, Kluwer/Plenum, New York, 2002.

    [7] Isakov, Victor. Inverse problems for partial di erential equations. Second edition. Applied Mathematical Sciences, 127. Springer, New York, 2006. xiv+344 pp.

    [8] Isakov, Victor; Nachman, Adrian I. Global uniqueness for a twodimensional semilinear elliptic inverse problem. Trans. Amer. Math. Soc. 347 (1995), no. 9, 33753390.

    [9] Kang, Kyeonbae; Nakamura, Gen. Identi cation of nonlinearity in a conductivity equation via the Dirichlet-to-Neumann map. Inverse Problems 18 (2002), no. 4, 10791088.

    [10] Katchalov, Alexander; Kurylev, Yaroslav; Lassas, Matti. Inverse boundary spectral problems. Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Mathematics, 123. Chapman & Hall/CRC, Boca Raton, FL, 2001.

  • Metrics
Share - Bookmark