# Inverse problem for a one-dimensional dynamical Dirac system (BC-method)

M. I. Belishev, V. S. Mikhailov

Результат исследований: Научные публикации в периодических изданияхстатья

### Выдержка

A forward problem for the Dirac system is to find u = ((u1(x, t))(u2(x,t))) obeying iu(t) + ((0) (1) (-1 0))u(x) + ((p) (q) (q) (-p))u = 0 for x> 0, t> 0; u( x, 0) = ((0) (0)) for x >= 0, and u(1)(0, t) = f( t) for t > 0, with the real p = p(x), q = q( x). An input-output map R: u(1)( 0, .) double right arrow u2( 0, .) is of the convolution form Rf = if + r * f, where r = r( t) is a response function. By hyperbolicity of the system, for any T > 0, function r I-0 0, given r I-0

Язык оригинала Английский 125013 26 Inverse Problems 30 12 https://doi.org/10.1088/0266-5611/30/12/125013 Опубликовано - дек 2014

### Цитировать

Belishev, M. I. ; Mikhailov, V. S. / Inverse problem for a one-dimensional dynamical Dirac system (BC-method). В: Inverse Problems. 2014 ; Том 30, № 12.
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Inverse problem for a one-dimensional dynamical Dirac system (BC-method). / Belishev, M. I.; Mikhailov, V. S.

В: Inverse Problems, Том 30, № 12, 125013, 12.2014.

Результат исследований: Научные публикации в периодических изданияхстатья

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AU - Belishev, M. I.

AU - Mikhailov, V. S.

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N2 - A forward problem for the Dirac system is to find u = ((u1(x, t))(u2(x,t))) obeying iu(t) + ((0) (1) (-1 0))u(x) + ((p) (q) (q) (-p))u = 0 for x> 0, t> 0; u( x, 0) = ((0) (0)) for x >= 0, and u(1)(0, t) = f( t) for t > 0, with the real p = p(x), q = q( x). An input-output map R: u(1)( 0, .) double right arrow u2( 0, .) is of the convolution form Rf = if + r * f, where r = r( t) is a response function. By hyperbolicity of the system, for any T > 0, function r I-0 0, given r I-0

AB - A forward problem for the Dirac system is to find u = ((u1(x, t))(u2(x,t))) obeying iu(t) + ((0) (1) (-1 0))u(x) + ((p) (q) (q) (-p))u = 0 for x> 0, t> 0; u( x, 0) = ((0) (0)) for x >= 0, and u(1)(0, t) = f( t) for t > 0, with the real p = p(x), q = q( x). An input-output map R: u(1)( 0, .) double right arrow u2( 0, .) is of the convolution form Rf = if + r * f, where r = r( t) is a response function. By hyperbolicity of the system, for any T > 0, function r I-0 0, given r I-0

KW - one-dimensional dynamical Dirac system

KW - controllability

KW - determination of potential

KW - characterization of inverse data

KW - OPERATORS

U2 - 10.1088/0266-5611/30/12/125013

DO - 10.1088/0266-5611/30/12/125013

M3 - статья

VL - 30

JO - Inverse Problems

JF - Inverse Problems

SN - 0266-5611

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