Filters

2006 - 200932010 - 20164

More filters

20197
Reset filters

Settings

Author: Yamamoto, Masahiro × WGL Institute: WIAS ×

Search Results

Now showing 1 - 7 of 7
  • Thumbnail Image
    Item
    Uniqueness in determining polyhedral sound-hard obstacles with a single incoming wave
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Elschner, Johannes; Yamamoto, Masahiro
    We consider the inverse acoustic scattering problem of determining a sound-hard obstacle by far field measurements. It is proved that a polyhedral scatterer in $R^n, nge 2$, consisting of finitely many solid polyhedra, is uniquely determined by a single incoming plane wave.
  • Thumbnail Image
    Item
    Exact controllability on a curve for a semilinear parabolic equation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Hömberg, Dietmar; Yamamoto, Masahiro
    Motivated by the growing number of industrially important laser material treatments we investigate the controllability on a curve for a semilinear parabolic equation. We prove the local exact controllability and a global stability result in the twodimensional setting. As an application we consider the control of laser surface hardening. We show that our theory applies to this situation and present numerical simulations for a PID control of laser hardening. Moreover, the result of an industrial case study is presented confirming that the numerically derived temperature in the hot-spot of the laser can indeed be used as set-point for the machine-based process control.
  • Thumbnail Image
    Item
    Single logarithmic conditional stability in determining unknown boundaries
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Elschner, Johannes; Hu, Guanghui; Yamamoto, Masahiro
    We prove a conditional stability estimate of log-type for determining unknown boundaries from a single Cauchy data taken on an accessible subboundary. Our approach relies on new interior and boundary estimates derived from the Carleman estimate for elliptic equations. A local stability result for target identification of an acoustic sound-soft scatterer from a single far-field pattern is also obtained.
  • Thumbnail Image
    Item
    Uniqueness in inverse elastic scattering with finitely many incident waves
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Elschner, Johannes; Yamamoto, Masahiro
    We consider the third and fourth exterior boundary value problems of linear isotropic elasticity and present uniqueness results for the corresponding inverse scattering problems with polyhedral-type obstacles and a finite number of incident plane elastic waves. Our approach is based on a reflection principle for the Navier equation.
  • Thumbnail Image
    Item
    Uniqueness in inverse elastic scattering from unbounded rigid surfaces of rectangular type
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Elschner, Johannes; Hu, Guanghui; Yamamoto, Masahiro
    Consider the two-dimensional inverse elastic scattering problem of recovering a piecewise linear rigid rough or periodic surface of rectangular type for which the neighboring line segments are always perpendicular.We prove the global uniqueness with at most two incident elastic plane waves by using near-field data. If the Lamé constants satisfy a certain condition, then the data of a single plane wave is sufficient to imply the uniqueness. Our proof is based on a transcendental equation for the Navier equation, which is derived from the expansion of analytic solutions to the Helmholtz equation. The uniqueness results apply also to an inverse scattering problem for non-convex bounded rigid bodies of rectangular type.
  • Thumbnail Image
    Item
    Parameter identification in non-isothermal nucleation and growth processes
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Hömberg, Dietmar; Lu, Shuai; Sakamoto, Kenichi; Yamamoto, Masahiro
    We study non-isothermal nucleation and growth phase transformations, which are described by a generalized Avrami model for the phase transition coupled with an energy balance to account for recalescence effects. The main novelty of our work is the identification of temperature dependent nucleation rates. We prove that such rates can be uniquely identified from measurements in a subdomain and apply an optimal control approach to develop a numerical strategy for its computation.
  • Thumbnail Image
    Item
    Uniqueness for an inverse problem for a nonlinear parabolic system with an integral term by one-point Dirichlet data
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Hömberg, Dietmar; Lu, Shuai; Yamamoto, Masahiro
    We consider an inverse problem arising in laser-induced thermotherapy, a minimally invasive method for cancer treatment, in which cancer tissues is destroyed by coagulation. For the dosage planning quantitatively reliable numerical simulation are indispensable. To this end the identification of the thermal growth kinetics of the coagulated zone is of crucial importance. Mathematically, this problem is a nonlinear and nonlocal parabolic heat source inverse problem. We show in this paper that the temperature dependent thermal growth parameter can be identified uniquely from a one-point measurement.