Inverse Problems for Parabolic Equations

Alemdar Hasanov Hasanoğlu and Vladimir G. Romanov
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Alemdar Hasanov Hasanoğlu: University of Kocaeli, Department of Mathematics
Vladimir G. Romanov: Sobolev Institute of Mathematics

Chapter Chapter 6 in Introduction to Inverse Problems for Differential Equations, 2021, pp 171-211 from Springer

Abstract: Abstract This Chapter deals with inverse coefficient problems for linear second-order 1D parabolic equations. We establish, first, a relationship between solutions of direct problems for parabolic and hyperbolic equations. Then using the results of Chap. 3 we derive solutions of the inverse problems for parabolic equations through the corresponding solutions of inverse problems for hyperbolic equations, using the Laplace transform. In the final part of this chapter, we study the relationship between the inverse problems for parabolic equation and inverse spectral problems.

Date: 2021
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DOI: 10.1007/978-3-030-79427-9_6

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