Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 28, pp. 1-8.

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

Author: Waseem Ghazi Alshanti (Al Zaytoonah Univ., Amman, Jordan)

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.

Submitted August 21, 2023. Published March 29, 2024.
Math Subject Classifications: 35E99, 47B01.
Key Words: Partial differential equations; tensor product of Banach spaces; atomic solution.