Multidimensional Inverse and Ill-Posed Problems for Differential Equations
Multidimensional Inverse and Ill-Posed Problems for Differential Equations
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微分方程的多维逆问题和病态问题
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Y. Anikonov
中科院分区：
文献类型：
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作者：
Y. Anikonov
第1部分算子方程和逆问题：准单调性的定义，双曲型方程反问题的唯一性定理地震学多维逆运动学问题关于Fredholm和沃尔泰拉第一-一类抛物型方程反问题解的存在唯一性发展方程多维反问题中的方程公式。第二部分动力学方程的反问题：动力学方程动力学方程反问题的例子一维反问题多维反问题动力学方程反问题解的唯一性定理一般唯一性定理“冗余”方程的影响分离微分和积分微分恒等式问题解-存在性问题是数学生物学的一个逆问题。第三部分大问题中的凸曲面几何与散射理论的反问题：散射理论的几何问题，第一类积分方程，唯一性，存在性，稳定性。第4部分积分几何：反演公式的唯一性和可解性的一些应用黎曼空间的结构和积分几何的问题积分几何中的问题的可解性积分沿着测地线。
Part 1 Operator equations and inverse problems: definition of quasimonotonicity, the uniqueness theorem inverse problems for hyperbolic equations multidimensional inverse kinematic problems of seismics on the uniqueness of the solution of the Fredholm and Volterra first-kind integral equations on the uniqueness of a solution of integral equations of the first kind with entire kernel existence and uniqueness of a solution to an inverse problem for a parabolic equation formulas in multidimensional inverse problems for evolution equations. Part 2 Inverse problems for kinetic equations: kinetic equations an example of an inverse problems for kinetic equation one-dimensional inverse problems multidimensional inverse problems an uniqueness theorem for the solution of an inverse problem for a kinetic equation the general uniqueness theorem the effect of the "redundant" equation problem of separation differential and integro-differential identities solution-existence problems an inverse problem of mathematical biology. Part 3 Geometry of convex surfaces in the large and inverse problems of scattering theory: geometrical question of scattering theory integral equation of the first kind uniqueness existence stability. Part 4 Integral geometry: inversion formulas the uniqueness and solvability some applications the structure of Riemann spaces and problems of the integral geometry the solvability of a problem in integral geometry by integration along geodesics.