Anharmonic semigroups and applications to global well-posedness of nonlinear heat equations
In this work we consider the semigroup e−tAk,ℓγ for γ > 0 associated to an anharmonic oscillator of the form Ak,ℓ=(−Δ)ℓ+|x|2k where k, ℓ are integers ≥1. By introducing a suitable Hörmander metric on the phase-space we analyze the semigroup e−tAk,ℓγ within the framework of Hörmander S(M, g) classes and obtain mapping properties in the scale of modulation spaces Mp,q,0<p,q≤∞, with respect to an anharmonic modulation weight. As an application, we apply the obtained bounds to establish the well-posedness for the nonlinear heat equation associated with Ak,ℓγ. It is worth noting that the results presented in this paper are novel, even in the case where γ = 1.
Authors
- Michael Ruzhansky (ORCID: https://orcid.org/0000-0001-8633-5570)
- Marianna Chatzakou (ORCID: https://orcid.org/0000-0003-0853-3007)
- Julio Delgado (ORCID: https://orcid.org/0000-0001-6329-9060)
- Vishvesh Kumar (ORCID: https://orcid.org/0000-0003-4799-9029)
- Duván Cardona (ORCID: https://orcid.org/0000-0002-8148-2624)
Institutions
- Queen Mary University of London (GB)
- Ghent University (BE)
- Universidad del Valle (CR)
- Universidad del Valle (NI)
- Universidad del Valle (CO)
Publication Details
- Journal
- Journal of Mathematical Physics
- Published
- 2025-08-01
- DOI
- https://doi.org/10.1063/5.0219555
- Primary Topic
- Stability and Controllability of Differential Equations
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Fonds Wetenschappelijk Onderzoek
- Universiteit Gent
- Universidad del Valle
- Vlaamse regering
- Engineering and Physical Sciences Research Council
- Bijzonder Onderzoeksfonds UGent