Analytical Solution for a Non-Self-Adjoint and Non-Local-Boundary Value Problem Including a Partial Differential Equation with a Complex Constant Coefficient
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In this paper, we investigate an initial-boundary value problem for a partial differential equation with a complex constant coefficient and non-local-boundary conditions whose related spectral problem is a non-self-adjoint-boundary value problem. For this problem, we first derive the related spectral problem. Then the formal and analytical solution were formulated by using eigenfunctions of the related spectral problem. Finally, the existence, uniqueness and convergence of the series solution will be proved.
KeywordsPartial differential equations Non-local-boundary value problem Self-adjoint problem Non-self-adjoint operators Fundamental solutions
Mathematics Subject Classification (2010)35A01 35A08 65N25
The authors are thankful to the honorable referee for his helpful and useful suggestions to improve the manuscript.
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