General Mathematics

    

On the Uniqueness of Solutions to the Cauchy Problem for Systems of Linear Differential Equations with Partial Derivatives

Authors: Igor Shchitov

This article presents examples of linear partial differential equations with analytic coefficients and system of such equations for which the solutions to the Cauchy problem in the class of continuously differentiable functions are non-unique. More precisely, the time during which the analytical solution to the Cauchy problem remains unique is finite for such equations and system,after which this solution may even transform into one of many possible solutions. These solutions may have unusual properties.Key words: systems of linear partial differential equations; analytical coefficients; Cauchy problem; Holmgren’s theorem; uniqueness of solution.

Comments: 6 Pages.

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[v1] 2026-10-10 00:36:23

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