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

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.