Solutions of linear and non-linear partial differential equations by means of tensor product theory of Banach space

Authors

  • Waseem Ghazi Alshanti Al Zaytoonah Univ., Amman, Jordan

DOI:

https://doi.org/10.58997/ejde.2024.28

Keywords:

Partial differential equations; tensor product of Banach spaces; atomic solution

Abstract

In this article, we introduce an analytical method for solving both non-separable linear and non-linear partial differential equations, for which separation of variables method does not work. This method is based on the theory of tensor product in Banach spaces coupled with some properties of atoms operators. We provide some illustrative examples.

For more information see https://ejde.math.txstate.edu/Volumes/2024/28/abstr.html

References

W. G. Alshanti, I. M. Batiha, A. Alshanty; Atomic Solutions of Partial Differential Equations via Tensor Product Theory of Banach Spaces. Contemp. Math., 4 2 (2023), 286.295.

W. G. Alshanti, I. M. Batiha, M. Abu Hammad, R. Khalil; A novel analytical approach for solving partial differential equations via a tensor product theory of Banach spaces. Partial Differ. Equ. Appl. Math., 8 (2023), 100531.

W. G. Alshanti, I. M. Batiha, A. Alshanty, R. Khalil; Tensor Product of Banach Spaces and Atomic Solutions of Partial Differential Equations. Int. J. Math. Comput. Sci., 19(3) (2024), 903-16.

I. Batiha, S. Njadat, R. Batyha, A. Zraiqat, A. Dababneh, S. Momani; Design fractionalorder PID controllers for single-joint robot arm model. Int. J. Advance Soft Compu. Appl., 14(2) (2022), 97.114.

I. Batiha, J. Oudetallah, A. Ouannas, A. Al-Nana, I. Jebril; Tuning the fractional-order PIDcontroller for blood glucose level of diabetic patients. Int. J. Advance Soft Compu. Appl., 13(2) (2021), 1.10.

J. Diestel, J.J. Uhl, Jr; Vector Measures, American Mathematical Society, Providence, Rhode Island, 1977.

L. Evans; Partial differential equations, American Mathematical Society, Providence, Rhode Island, 2010.

G. Evans, J. Blackledge, P. Yardley; Analytic Methods for Partial Differential Equations, Springer Science and Business Media, Berlin, Heidelberg, 2012.

R. Khalil; Isometries of Lp..Lp. Tam. J. Math.. 16 (1985), 77.85.

R. Khalil, L. Abdullah; Atomic solution of certain inverse problems. Eur. J. Pure Appl. Math.. 34 (2010), 725.729.

W. Light, E. W. Cheney; Approximation Theory in Tensor Product Spaces, Springer Science and Business Media, Berlin, Heidelberg, 1985.

J. Peiro, S. Sherwin; Finite Difference, Finite Element and Finite Volume Methods for Partial Differential Equations. In Handbook of Materials Modeling: Methods, Dordrecht: Springer Netherlands, 2005. 2415.2446

R. Ryan; Introduction to Tensor Products of Banach Spaces, Springer, London, 2002.

F. C. Sanchez, R. Garc¢¥©¥a; The bidual of a tensor product of Banach spaces. Rev. mat. Iberoam. 213 (2005), 843.861.

R. Schatten; A Theory of Cross-Spaces, Princeton University Press, New Jersey, United States, 1950.

Downloads

Published

2024-03-29

Issue

Section

Articles

Categories

How to Cite

Solutions of linear and non-linear partial differential equations by means of tensor product theory of Banach space. (2024). Electronic Journal of Differential Equations, 2024(01-??), No 28, 1-8. https://doi.org/10.58997/ejde.2024.28