Developing an approach to the question of existence, uniqueness and stability of solutions, this work presents a systematic elaboration of the theory of inverse problems for all principal types of partial differential equations. It covers up-to-date methods of linear and nonlinear analysis, the theory of differential equations in Banach spaces, applications of functional analysis, and semigroup theory.Theorem 1.1.7 There exists a solution u 6 V^(Qr) of problem (1.1.43)- (1.1.45) for ... (1968) or Duvant and Lions (1972)) Let F 6 L2(QT), a C L2(tt), b 6 W221(QT) and let the coefficient C(x) alt; 0 for x E n ; a(x) agt; 0 for x 6 ft ; b(x, t)agt;Q for (x, t)anST; F(x anbsp;...
|Title||:||Methods for Solving Inverse Problems in Mathematical Physics|
|Author||:||Global Express Ltd. Co., Aleksey I. Prilepko, Dmitry G. Orlovsky, Igor A. Vasin|
|Publisher||:||CRC Press - 2000-03-21|