A novel analytical approach for solving partial differential equations via a tensor product theory of Banach spaces

Waseem G. Alshanti; Iqbal M. Batiha; Ma'mon Abu Hammad; Roshdi Khalil

doi:10.1016/j.padiff.2023.100531

A novel analytical approach for solving partial differential equations via a tensor product theory of Banach spaces

Waseem G. Alshanti
, Iqbal M. Batiha
, Ma'mon Abu Hammad
, Roshdi Khalil

Nonlinear Dynamic Research Centre (NDRC)

Al-Zaytoonah University of Jordan
University of Jordan

Research output: Contribution to journal › Article › peer-review

28 Scopus citations

Abstract

In this paper, we aim to propose a novel analytical method for obtaining atomic solutions to partial differential equations. A theory of tensor products in Banach spaces is utilized and some properties of atom operators are studied to achieve our goals. The proposed scheme is demonstrated through illustrative examples of inhomogeneous partial differential equations. The approach is indeed quite direct and effective in exactly solving partial differential equations.

Original language	English
Article number	100531
Journal	Partial Differential Equations in Applied Mathematics
Volume	8
DOIs	https://doi.org/10.1016/j.padiff.2023.100531
State	Published - Dec 2023

Keywords

Atomic solution
Partial differential equations
Tensor product of Banach space

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10.1016/j.padiff.2023.100531

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title = "A novel analytical approach for solving partial differential equations via a tensor product theory of Banach spaces",

abstract = "In this paper, we aim to propose a novel analytical method for obtaining atomic solutions to partial differential equations. A theory of tensor products in Banach spaces is utilized and some properties of atom operators are studied to achieve our goals. The proposed scheme is demonstrated through illustrative examples of inhomogeneous partial differential equations. The approach is indeed quite direct and effective in exactly solving partial differential equations.",

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AU - Hammad, Ma'mon Abu

AU - Khalil, Roshdi

PY - 2023/12

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AB - In this paper, we aim to propose a novel analytical method for obtaining atomic solutions to partial differential equations. A theory of tensor products in Banach spaces is utilized and some properties of atom operators are studied to achieve our goals. The proposed scheme is demonstrated through illustrative examples of inhomogeneous partial differential equations. The approach is indeed quite direct and effective in exactly solving partial differential equations.

KW - Atomic solution

KW - Partial differential equations

KW - Tensor product of Banach space

UR - https://www.scopus.com/pages/publications/85162100389

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JO - Partial Differential Equations in Applied Mathematics

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A novel analytical approach for solving partial differential equations via a tensor product theory of Banach spaces

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