ON SOLVABILITY OF THE INTEGRODIFFERENTIAL HYPERBOLIC EQUATION WITH PURELY NONLOCAL CONDITIONS

• Published in: Acta mathematica scientia Vol. 35; no. 3; pp. 601 - 609
• Main Authors: MERAD, Ahcene, BOUZIANI, Abdelfatah, OZEL, Cenap, KILIÇMAN, Adem
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.05.2015; Department of Mathematics, Larbi Ben M'hidi University, Oum El Bouaghi, Algeria%Department of Mathematics, Faculty of Science, Dokuz Eylul University 35160 Buca/I.zmir, Turkey%Department of Mathematics and Institute for Mathematical Research,Universiti Putra Malaysia, UPM, Serdang, Selangor, 43400, Malaysia
• Subjects: 34A12; 35L10; 44A10; approximate solution; Integro-differential hyperbolic equation; nonlocal purely conditions; Stehfest算法; 双曲型方程; 变换方法; 存在唯一性; 拉普拉斯变换; 积分方程; 连续依赖性; 非局部条件; approximate solution; 44A10; Integro-differential hyperbolic equation; nonlocal purely conditions; 34A12; 35L10
• ISSN: 0252-9602; 1572-9087
• DOI: 10.1016/S0252-9602(15)30006-0

In this study, we prove the existence, uniqueness, and continuous dependence upon the data of solution to integro-differential hyperbolic equation with purely nonlocal （integral） conditions. The proofs are based on a priori estimates and Laplace transform method. Finally, we obtain the solution using a numerical technique （Stehfest algorithm） by inverting the Laplace transform.