TY  - JOUR
T1  - Periyodik Sınır Koşullu Lineer Olmayan Hiperbolik Problemin Yakınsaklık Analizi
TT  - Convergence Analysis of Nonlinear Hyperbolic Problem with Periodic Boundary Conditions
AU  - Bağlan, İrem
AU  - Yernazar, Akbala
PY  - 2024
DA  - December
Y2  - 2024
JF  - ADÜ Fen ve Mühendislik Bilimleri Dergisi
JO  - adufmbd
PB  - Aydin Adnan Menderes University
WT  - DergiPark
SP  - 84
EP  - 91
VL  - 1
IS  - 2
LA  - tr
AB  - Bu çalışmada, periyodik sınır koşullarına sahip bir boyutlu lineer olmayan hiperbolik denklemi için zamana bağlı katsayıların belirlenmesine yönelik bir ters problem ele alınmıştır. Periyodik sınır koşullar sinüs, kosinüs biçimindeki özfonksiyonları içerir ve her özdeğer iki özfonksiyona karşılık geldiği için çözüm sürecini karmaşıklaştırmaktadır. Bu tür lokal olmayan sınır koşullarına sahip alanlarda sınır değer problemlerini çözmekte etkili olan genelleştirilmiş Fourier yöntemi kullanılmıştır. Picard ardışık yaklaşımlar yöntemi ile çözümün varlığı, yakınsaklığı ve tekliği kanıtlanmıştır.
KW  - Ters problem
KW  - Hiperbolik denklem
KW  - Periyodik sınır koşulu
KW  - Fourier yöntemi
N2  - In this paper, an inverse problem for the determination of time-dependent coefficients for a one-dimensiоnаl nonlinеаr hypеrbоlic equation with periоdic bоundаrу conditions is considered. The periodic boundary conditions involve eigenfunctions in the form of sine, cosine and each eigenvalue corresponds to two eigenfunctions, which complicates the solution process. The generalised Fourier method, effective for solving boundary value problems in domains with such non-local boundary conditions, is used. The existence, uniqueness and convergence of the solution are proved using the Picard method of successive approximations.
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UR  - https://dergipark.org.tr/en/pub/adufmbd/article/1594219
L1  - https://dergipark.org.tr/en/download/article-file/4406932
ER  -