On one method for solving a mixed boundary value problem for a parabolic type equation using operators $\mathbb{AT}_{\lambda,j}$

A. Yu. Trynin

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2024), pp. 59-80

Résumé

A new method for obtaining a generalized solution of a mixed boundary value problem for a parabolic equation with boundary conditions of the third kind and a continuous initial condition is proposed. Generalized functions are understood in the sense of a sequential approach. The representative of the class of sequences, which is a generalized function, is obtained using the function interpolation operator, constructed using solutions of the Cauchy problem. The solution is obtained in the form of a series that converges uniformly inside the domain of the solution.

Détail

Keywords: mixed boundary value problem, generalized solution, sinc approximation
Mots-clés : uniform convergence.

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