Journals / Contemporary Analysis and Applied Mathematics / 2014 / Cilt: 2 - Sayı: 2

Çok boyutlu bir uzayda Cauchy problemi üzerine

On the Cauchy problem in a multidimensional space

Pages
212–223
Publication Date
2022-10-11
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The weak solvability of the Cauchy problem and uniqueness of the solution are proved.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In the present paper, the Cauchy problem for a multidimensional hyperbolic equation is studied.
📊
Key Findings & Data:In the present paper, the Cauchy problem for a multidimensional hyperbolic equation is studied.
💡
Conclusion & Impact:The weak solvability of the Cauchy problem and uniqueness of the solution are proved.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In the present paper, the Cauchy problem for a multidimensional hyperbolic equation is studied. The weak solvability of the Cauchy problem and uniqueness of the solution are proved.

Özet

Bu makalede çok boyutlu hiperbolik denklem için Cauchy problemi çalışıldı. Cauchy probleminin zayf çözülebilirliği ve çözümün tekliği ispat edildi.

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Cite This Article

SOLTANOV, H. (2022). Çok boyutlu bir uzayda Cauchy problemi üzerine. Contemporary Analysis and Applied Mathematics, Cilt: 2 - Sayı: 2, 212–223. https://ajindex.com/articles/476475

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References (13)

  1. H. O. Fattorini, Second Order Linear Differential Equations in Banach Spaces, Elsevier Science Publishing Company, North-Holland, 1985
  2. J. A. Goldstein, Semigroups of Linear Operators and Applications, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, New York, 1985
  3. V. V. Vasilev, S. G. Krein, S. Piskarev, Operator Semigroups, Cosine Operator Functions, and Linear Differential Equations, in: Mathematical Analysis, Vol. 28. (Russian), Itogi Nauki i Tekhniki, 204(1990), 87–202, Akad. Nauk SSSR Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1990. Translated in J. Soviet Math. 54, no. 4, 1042–1129, 1991
  4. A. Ashyralyev, P. E. Sobolevskii, New Difference Schemes for Partial Differential Equations, Operator Theory Advances and Applications, Birkh¨auser Verlag, Basel, Boston, Berlin, 2004
  5. A. Ashyralyev, P. E. Sobolevskii, Two new approaches for construction of the high order of accuracy difference schemes for hyperbolic differential equations, Discrete Dynamics in Nature and Society 2005 (2) (2005) 183-213
  6. A. Ashyralyev, H. O. Fattorini, On uniform difference schemes for second order singular perturbation problems in Banach spaces, SIAM J. Math. Analysis 23 (1) (1992) 29-54
  7. A. Ashyralyev, O. Yildirim, On the numerical solution of hyperbolic IBVP with high order stable difference schemes, Boundary Value Problems 2013 (Article ID 29) (2013) 1-34
  8. V. Pogorelenko, P. E. Sobolevskii, Hyperbolic equations in a Hilbert space, Sibirsk. Matem. Zh. 8 (1) (1967) 123-145
  9. A. Ashyralyev, M. E. Koksal, On the second order of accuracy difference scheme for hyperbolic equations in a Hilbert space, Numerical Functional Analysis and Optimization 26 (7-8) (2005) 739-772
  10. A. Ashyralyev, M. E. Koksal, On the Stability of the second order of accuracy difference scheme for hyperbolic equations, Discrete Dynamics in Nature and Society 2007 (Article ID 57491) (2007) 1-26
  11. A. Ashyralyev, M. E. Koksal, On the numerical solution of hyperbolic PDEs with variable space operator, Numerical Methods for Partial Differential Equations 25 (5) (2009) 1084- 1096
  12. A. Ashyralyev, M. E. Koksal, R. P. Agarwal, A difference scheme for cauchy problem for hyperbolic equation with self-adjoint operator, Math. Comput. Model. 52 (2010) 409-424
  13. A. Ashyralyev, M. E. Koksal, R. P. Agarwal, An operator-difference scheme for abstract Cauchy problems, Computer and Mathematics with Applications 61 (7) (2011) 1855-1872