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arXiv · 2504.21396

Square Root Operators and the Well-Posedness of Pseudodifferential Parabolic Models of Wave Phenomena

Matthias Ehrhardt·Jochen Glück·Pavel Petrov·Stefan Tappe
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Abstract

Pseudodifferential parabolic equations with an operator square root arise in wave propagation problems as a one-way counterpart of the Helmholtz equation. The expression under the square root usually involves a differential operator and a known function. We discuss a rigorous definition of such operator square roots and show well-posedness of the pseudodifferential parabolic equation by using the theory of strongly continuous semigroups. This provides a justification for a family of widely-used numerical methods for wavefield simulations in various areas of physics.

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Matthias Ehrhardt, Jochen Glück, Pavel Petrov, Stefan Tappe. 2025-04-30. Square Root Operators and the Well-Posedness of Pseudodifferential Parabolic Models of Wave Phenomena. https://doi.org/10.1016/j.aml.2025.109644

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