A Mixed Problem For Partial Differential Equations of Parabolic Type With Involution
DOI:
https://doi.org/10.58649/9vhfnj61Keywords:
Partial differential equations, parabolic equations, involution operator, mixed boundary value problem, Fourier method, eigenvalues, nonlocal problemsAbstract
This paper investigates a class of mixed boundary value problems for parabolictype partial differential equations incorporating an involution operator. We establish sufficient conditions ensuring the existence and uniqueness of classical solutions within an appropriate functional framework. Utilizing the method of separation of variables in conjunction with Fourier analysis, we construct explicit representations of solutions to the transformed problem. Our results contribute to the broader theory of differential equations with nonlocal features and offer insights into the analytical structure induced by the involution term.
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