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DOI: 10.46698/y0708-2078-6879-i
Averaging of Abstract Parabolic Equations with Multipoint Integral Boundary Conditions
Levenstam, V. B.
Vladikavkaz Mathematical Journal 2024. Vol. 26. Issue 4.
Abstract: A multipoint boundary value problem for an abstract parabolic equation with a rapidly time-oscillating nonlinear part is considered in the time interval. The operator \(-A\), where \(A\) is the senior stationary linear operator of the equation, is positive. The hypotheses are formulated in terms of the theory of semigroups and fractional powers of the operator \(-A\). Multipoint boundary conditions on a time interval contain integral terms. For the specified problem, which depends on a large parameter (high oscillation frequency), a limiting (averaged) multipoint boundary value problem is constructed and a limiting transition in the space of continuous vector functions over a time interval is justified. Thus, the Krylov-Bogolyubov averaging method is justified for abstract parabolic equations with multipoint boundary conditions. The results obtained are applicable to parabolic equations in a limited spatial
domain with multipoint boundary conditions over a time interval and some other problems of mathematical physics.
For citation: Levenstam, V. B. Averaging of Abstract Parabolic Equations with Multipoint Integral Boundary Conditions, Vladikavkaz Math. J., 2024, vol. 26, no. 4, pp. 95-104 (in Russian). DOI 10.46698/y0708-2078-6879-i
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