Inverse Problems for Partial Differential Equations
Inverse Problems for Partial Differential Equations
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DOI：
10.1515/9783110944631
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发表时间：
2002-01
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影响因子：
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通讯作者：
Y. Belov
中科院分区：
文献类型：
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作者：
Y. Belov
泛函分析和微分方程理论的辅助信息基本概念和符号不等式泛函分析的一些概念和定理一阶线性偏微分方程二阶抛物型方程的最大值原理弱逼近方法的例子归结为弱逼近方法的概念弱逼近方法的一般公式两个定理一个例子抛物型方程Cauchy数据的线性偏微分方程识别问题未知源函数未知最低系数未知系数一阶导数未知系数时间导数半线性抛物型方程Burgers型方程的反问题一个多-一维反问题转化为低维问题复合型方程组和抛物型方程源函数的识别问题解在t-下的性质>问题存在唯一性定理的陈述“总体上”问题解在t-下的性质>定常问题到定常问题的收敛解的唯一可解性抛物方程源函数的识别问题反问题解的稳定性抛物方程系数的确定问题及其解的一些性质问题的存在性和唯一性定理t-下解的“整体”性质双未知系数抛物型方程的一致边界条件非齐次超定条件输入数据的特殊形式某些反边界问题未知源函数非线性热方程小参数双曲型方程.
Auxiliary information from functional analysis and theory of differential equations the basic notions and notations inequalities some concepts and theorems of functional analysis linear partial differential equation of the first order the maximum principle for parabolic equations of second order the weak approximation method examples reducing to the concept of the weak approximation method general formulation of the weak approximation method two theorems - an example the linear partial differential equation identification problems for parabolic equations with Cauchy data the unknown source function the unknown lowest coefficient the unknown coefficient to the first order derivative an unknown coefficient to the time derivative inverse problem for a semilinear parabolic equation equations of Burgers type the splitting of one many-dimensional inverse problem into problems of lower dimension the identification of the source function for a system of composite type and parabolic equation the behaviour of the problem's solution under t-> the statement of the problem theorems of existence and uniqueness "on the whole" the behaviour of solution by t-> stationary problem convergence to the stationary problem solution unique solvability of the problem of identifying the source function for a parabolic equation the stabilization of the solution to the inverse problem the problem of determining the coefficient in a parabolic equation and some properties of its solution statement of the problem theorems of existence and uniqueness "on the whole" properties of solution under t-> two unknown coefficients of a parabolic type equation uniform boundary conditions inhomogeneous conditions of over-determination input data of the special form some inverse boundary problems unknown source function nonlinear heat equation hyperbolic equation with small parameter.