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Uniqueness and Stability in the Cauchy Problem

  • Victor Isakov
Chapter
  • 1.9k Downloads
Part of the Applied Mathematical Sciences book series (AMS, volume 127)

Abstract

In this chapter we formulate and in many cases prove results on the uniqueness and stability of solutions of the Cauchy problem for general partial differential equations. One of the basic tools is Carleman-type estimates. In Section 3.1 we describe the results for a simplest problem of this kind (the backward parabolic equation), where a choice of the weight function in Carleman estimates is obvious, and the method is equivalent to that of the logarithmic convexity. In Section 3.2 we formulate general conditional Carleman estimates and their simplifications for second-order equations, and we apply the results to the general Cauchy problem and give numerous counterexamples showing that the assumptions of positive results are quite sharp.

Keywords

Carleman Estimates Backward Parabolic Equation Lateral Cauchy Problem Strongly Pseudoconvex Tataru 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer International Publishing AG 2017

Authors and Affiliations

  • Victor Isakov
    • 1
  1. 1.Department of Mathematics and StatisticsWichita State UniversityWichitaUSA

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