Well-Posedness of SI Problem for an Elliptic Equation in a Banach Space with Mixed Boundary Conditions

In present study, we discuss the next source identification (SI) boundary value problem (BVP) for an elliptic equation $-v^{\prime\prime}(t)+Av(t)=g(t)+p,\quad t\in(0,T),$ $v^{\prime}(0)=\varphi,\quad v^{\prime}(T)=\psi,\quad v(\gamma)=\zeta$ in an arbitrary Banach space $E$ with a positive operator $A$. The exact inequalities for SI problem in several Hölder norms are established. Afterward, coercive stability inequalities for three multidimensional elliptic BVPs are established in apps.

Authors
Ashyralyev A. 1, 2, 3 , Ashyralyyev C.1, 4
Publisher
Pleiades Publishing
Number of issue
8
Language
Russian
Pages
3241-3249
Status
Published
Volume
44
Year
2023
Organizations
  • 1 Department of Mathematics, Bahcesehir University
  • 2 Peoples’ Friendship University of Russia (RUDN University)
  • 3 Institute of Mathematics and Mathematical Modeling
  • 4 Mirzo Ulugbek National University of Uzbekistan
Keywords
well-posedness; elliptic equations; stability; source identification; exact estimates; boundary value problem
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