Recovering Initial States in Semilinear Parabolic Problems from Time-Averages

Lina Sophie Schmitz; Christoph Walker

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arXiv · 2407.03829

Recovering Initial States in Semilinear Parabolic Problems from Time-Averages

Lina Sophie Schmitz·Christoph Walker

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Abstract

Well-posedness of certain semilinear parabolic problems with nonlocal initial conditions is shown in time-weighted spaces. The result is applied to recover the initial states in semilinear parabolic problems with nonlinearities of superlinear behavior near zero from small time-averages over arbitrary time periods.

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Lina Sophie Schmitz, Christoph Walker. 2024-07-04. Recovering Initial States in Semilinear Parabolic Problems from Time-Averages. https://arxiv.org/abs/2407.03829

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