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Two‐Rank and Atomic Solutions of a Bateman–Burgers Type Equation via Functional Analytic Methods

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  • Waseem Ghazi Alshanti
  • Ma’mon Abu Hammad
  • Roshdi Khalil

Abstract

In this paper, we derive both a two‐rank solution and an atomic solution for a Bateman–Burgers type partial differential equation. Specifically, we study an equation in which the second mixed derivative of the unknown function with respect to space and time, together with the second derivative in space, equals the second derivative in time. Using functional analysis techniques, particularly the Hahn–Banach theorem and tensor product theory, we construct explicit two‐rank and atomic solutions. These results illustrate how functional analytic tools provide alternative strategies for analyzing nonlinear equations where traditional separation of variables does not apply.

Suggested Citation

  • Waseem Ghazi Alshanti & Ma’mon Abu Hammad & Roshdi Khalil, 2025. "Two‐Rank and Atomic Solutions of a Bateman–Burgers Type Equation via Functional Analytic Methods," Journal of Applied Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jnljam:v:2025:y:2025:i:1:n:2323749
    DOI: 10.1155/jama/2323749
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    References listed on IDEAS

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    1. He, Ji-Huan & Wu, Xu-Hong, 2006. "Exp-function method for nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 700-708.
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