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Optimal recovery methods exact on trigonometric polynomials for the solution of the heat equation. (English. Russian original) Zbl 1512.35355

Math. Notes 113, No. 1, 116-128 (2023); translation from Mat. Zametki 113, No. 1, 118-131 (2023).
Summary: We consider the problem of the optimal recovery of solutions of the heat equation on the torus \(\mathbb{T}\) from a finite set of inaccurate Fourier coefficients of the initial temperature. In addition, accuracy conditions on subspaces of trigonometric polynomials of fixed degree are imposed on these methods.

MSC:

35K05 Heat equation
35C10 Series solutions to PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
42A10 Trigonometric approximation
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