Uniqueness Problems for Degenerating Equations and Nonclassical Problems:

ISBN-13: 9783110364163 / Angielski / Twarda / 2001 / 184 str.

S. P. Shishatskii; A. Asanov; E. R. Atamanov

Opis

The study of Cauchy problems for degenerating equations and systems is a wide and actively developing area. However, the majority deals mainly with Cauchy problems for hyperbolic equations and systems and characteristic Cauchy problems for parabolic equations and systems.
This volume in the "Inverse and Ill-Posed Problems Series presents the results that were obtained on uniqueness for the main (ill-posed in the regular case) Cauchy problems for equations of the second order with exponential degeneracy. The Cauchy problem for a degenerating elliptic equation, the noncharacteristic Cauchy problem, and the mixed problem with reversed time for a degenerating parabolic equation are considered. Stability estimates that guarantee conditional well-posedness of the considered Cauchy problems in terms of the inverse problems theory are given, along with uniqueness theorems.