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March 5, 2026Filomat0 citationsOpen Access

On existence and uniqueness of a solution of mixed problem for a class of non-classical equations

YMYu.A. MamedovVMV.Yu. Mastaliyev

Key Points

  • To investigate the existence and uniqueness of solutions for initial boundary value problems of equations with complex coefficients.
  • Analyzing equations that transition between parabolic and different types like Schrodinger and antiparabolic.
  • Applying Birkhoff's theorem to assess characteristics of roots of polynomials.
  • Established conditions under which solutions exist and are unique for the proposed equations.
  • Determined the behavior of the equations transitioning between types.

Abstract

Existence and uniqueness of the solution of initial boundary value problem for a class of equations with complex-valued coefficients is treated in this work. These equations behave like parabolic ones, though in time they may transform from parabolic to Schrodinger type or even to antiparabolic type. Note that for the equations of corresponding spectral problems the arguments of the roots of characteristic polynomials in the sense of Birkhoff are not constant.

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Cite This Study

Mamedov et al. (2025) studied this question.

synapsesocial.com/papers/69a91d8dd6127c7a504c075chttps://doi.org/10.2298/fil2519651m
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