Inverse Problems for Partial Differential Equations

ISBN: 9789067643580 出版年：2012 页码：220 Belov, Yurii Ya De Gruyter

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.