Inverse problems for equations of parabolic type.

*(English)*Zbl 1147.35110
Mathematical Studies Monograph Series 10. Lviv: VNTL Publishers (ISBN 966-7148-98-X/pbk). 238 p. (2003).

Due to the possibility of determination of physical properties for materials by means of mathematical computations without carrying out physical experiments, inverse problems conceived a wide practical application in: metallurgy, medicine, biology, cosmic exploring, ecology, etc.

The structure of this book is the following: it begins with an auxiliary chapter, which contains some tools of investigation with technical character, such as integral inequalities and Green functions. The third chapter is devoted to the linear inverse problems for parabolic equations with unknown non-homogeneous term. The next chapter deals with the determination of the time-dependent coefficient at the higher-order derivative in a one-dimensional parabolic equation. In Chapter 5, a possibility of simultaneous determination of two coefficients dependent on different variables is established. The main objective of the last chapter is the explicit construction of the solution of the non-characteristic Cauchy problem for the heat equation.

The structure of this book is the following: it begins with an auxiliary chapter, which contains some tools of investigation with technical character, such as integral inequalities and Green functions. The third chapter is devoted to the linear inverse problems for parabolic equations with unknown non-homogeneous term. The next chapter deals with the determination of the time-dependent coefficient at the higher-order derivative in a one-dimensional parabolic equation. In Chapter 5, a possibility of simultaneous determination of two coefficients dependent on different variables is established. The main objective of the last chapter is the explicit construction of the solution of the non-characteristic Cauchy problem for the heat equation.

Reviewer: Ruxandra Stavre (Bucureşti)