Recovering Initial States in Semilinear Parabolic Problems from Time-Averages

2024/07/04 by Lina Sophie Schmitz, Schmitz, Lina Sophie, Christoph Walker +1 · 2 citations
Mathematics · Computer Science · Engineering · #Numerical methods in inverse problems #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics

paper · pdf · doi:10.48550/arxiv.2407.03829

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.

Cited by

• Solutions to Second-Order Nonlocal Evolution Equations Governed by Non-Autonomous Forms
• Recovering Initial States in Certain Quasilinear Parabolic Problems from Time Averages

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