KaydedilenlerDerginizi ekleyin

Dergiler / Sakarya University Journal of Science / 2026 / Volume: 28 Issue: 2

Schwarz Problem for Model Partial Differential Equations with One Complex Variable

Bahriye Karaca(MALTEPE UNIVERSITY)0000-0003-4463-8180
Sayfa
—
Yayın Tarihi
2024-04-30
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

However, by incorporating additional boundary conditions, it becomes feasible to obtain a unique solution for problem concerning n-order equations, effectively rendering it a well-posed problem.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:This paper investigates the Schwarz problem.
📊
Temel Bulgular & Veri:The findings demonstrate that the Schwarz problem for an n-order equation, when equipped with solely one boundary condition, exhibits an infinite number of solutions.
💡
Sonuç & Katkı:However, by incorporating additional boundary conditions, it becomes feasible to obtain a unique solution for problem concerning n-order equations, effectively rendering it a well-posed problem.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Schwarz Problem · Complex model homogeneous partial differential equation · Complex model inhomogeneous partial differential equations

Abstract

This paper investigates the Schwarz problem. Initially, the focus lies on analyzing the problem for the first, second orders. Subsequently, attention shifts towards studying the same problem for equations of higher order. In the realm of second-order equations, the Schwarz problem is specifically examined for some operators; Laplace, Bitsadze and its complex conjugate. The findings demonstrate that the Schwarz problem for an n-order equation, when equipped with solely one boundary condition, exhibits an infinite number of solutions. However, by incorporating additional boundary conditions, it becomes feasible to obtain a unique solution for problem concerning n-order equations, effectively rendering it a well-posed problem.

🔖

Bu Makaleye Atıf Yap

Karaca, B. (2024). Schwarz Problem for Model Partial Differential Equations with One Complex Variable. Sakarya University Journal of Science, Volume: 28 Issue: 2. https://doi.org/10.16984/saufenbilder.1390617

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (8)

  1. H. Begehr, “Boundary Value Problems in Complex Analysis Ⅰ, Ⅱ,” Boletin de la Asosiacion, vol. Ⅻ, no. 2, pp. 65-85, 217-250, 2005.
  2. B. Karaca, “Dirichlet Problem for Complex Model Partial Differential Equations,” Complex Variables and Elliptic Equations, vol. 65, no. 10, pp. 1748-1762, 2020.
  3. H. Begehr, S. Burgumbayeva, B. Shupeyeva, “Harmonic Green Functions for a Plane Domain With Two Touching Circles As Boundary,” Advanced Mathematical Models & Applications, vol. 3, no. 1, pp. 18-29, 2018.
  4. Ü. Aksoy, AO. Çelebi, “Schwarz Problem for Higher Order Linear Equations in a Polydisc,” Complex Variables and Elliptic Equations, vol. 62, no. 10, pp. 1558-1569, 2017.
  5. M. Akel, M. Hidan, M. Abdalla, “Complex Boundary Value Problems for the Cauchy–Riemann Operator on a Triangle,” Fractals, vol. 30, no. 10, pp. 1-15, 2022.
  6. M. Akel, H. Begehr, A. Mohammed, “A Neumann Problem for the Polyanalytic Operator in Planar Domains with Harmonic Green Function,” Applicable Analysis, vol. 101, no. 11, pp. 3816-3824, 2022.
  7. H. Begehr, S. Burgumbayeva, A. Dauletkulova, H. Lin, “Harmonic Green Functions for the Almaty Apple,” Complex Variables and Elliptic Equations, vol. 65, no. 11, pp. 1814-1825, 2020.
  8. Ü. Aksoy, H. Begehr, AO. Çelebi, “Schwarz Problem for Higher‐Order Complex Partial Differential Equations in the Upper Half Plane,” Mathematische Nachrichten, vol. 292, no. 6, pp. 1183-1193, 2019.