О разрешимости обратных задач восстановления параметров в эллиптических уравнениях

Translated title of the contribution: On the solvability of the inverse problems of parameter recovery in elliptic equations

Research output: Contribution to journalArticlepeer-review

Abstract

We study solvability of the inverse problems of finding, alongside the solution u(x, t), the positive parameter a in the differential equations utt + αΔu - Βu = f(x, t), αutt + Δu - Βu = f(x, t) where t ε (0, T), x = (x1,…, xn) ε Ω ⊂ Rn, and Δ the Laplace operator in variables x1,…, xn. As a complement to the boundary conditions defining a well-posed boundary value problem for elliptic equations, we use the conditions of the linear final integral overdetermination. We prove the existence and uniqueness theorems for regular solutions, those having all generalized in the S. L. Sobolev sense derivatives in the equation.

Translated title of the contributionOn the solvability of the inverse problems of parameter recovery in elliptic equations
Original languageRussian
Article number2
Pages (from-to)14-29
Number of pages16
JournalMathematical Notes of NEFU
Volume27
Issue number4
DOIs
Publication statusPublished - 2020

Keywords

  • Elliptic equation
  • Existence
  • Final-integral overdetermination condition
  • Regular solution
  • Uniqueness
  • Unknown coefficient

OECD FOS+WOS

  • 1.01 MATHEMATICS
  • 1.02 COMPUTER AND INFORMATION SCIENCES

State classification of scientific and technological information

  • 27 MATHEMATICS

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