Anharmonic semigroups and applications to global well-posedness of nonlinear heat equations
- Author
- Duvan Cardona Sanchez (UGent) , Marianna Chatzakou (UGent) , Julio Delgado, Vishvesh Kumar (UGent) and Michael Ruzhansky (UGent)
- Organization
- Project
- Abstract
- In this work we consider the semigroup e(k,& ell;)(-tA)(gamma) for gamma > 0 associated to an anharmonic oscillator of the form A(k,& ell;)=(-Delta)& ell;+|x|2k where k, & ell; are integers >= 1. By introducing a suitable H & ouml;rmander metric on the phase-space we analyze the semigroup e(-t)A(k,& ell;)(gamma) within the framework of Hormander S(M, g) classes and obtain mapping properties in the scale of modulation spaces M-p,M-q, 0 < p,q <= infinity 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 A(k,& ell;)(gamma) It is worth noting that the results presented in this paper are novel, even in the case where gamma = 1.
- Keywords
- PSEUDODIFFERENTIAL-OPERATORS, SPACES, BOUNDEDNESS, SCHRODINGER
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-01KAKR6MCC6DGVAC43PBY035FY
- MLA
- Cardona Sanchez, Duvan, et al. “Anharmonic Semigroups and Applications to Global Well-Posedness of Nonlinear Heat Equations.” JOURNAL OF MATHEMATICAL PHYSICS, vol. 66, no. 8, 2025, doi:10.1063/5.0219555.
- APA
- Cardona Sanchez, D., Chatzakou, M., Delgado, J., Kumar, V., & Ruzhansky, M. (2025). Anharmonic semigroups and applications to global well-posedness of nonlinear heat equations. JOURNAL OF MATHEMATICAL PHYSICS, 66(8). https://doi.org/10.1063/5.0219555
- Chicago author-date
- Cardona Sanchez, Duvan, Marianna Chatzakou, Julio Delgado, Vishvesh Kumar, and Michael Ruzhansky. 2025. “Anharmonic Semigroups and Applications to Global Well-Posedness of Nonlinear Heat Equations.” JOURNAL OF MATHEMATICAL PHYSICS 66 (8). https://doi.org/10.1063/5.0219555.
- Chicago author-date (all authors)
- Cardona Sanchez, Duvan, Marianna Chatzakou, Julio Delgado, Vishvesh Kumar, and Michael Ruzhansky. 2025. “Anharmonic Semigroups and Applications to Global Well-Posedness of Nonlinear Heat Equations.” JOURNAL OF MATHEMATICAL PHYSICS 66 (8). doi:10.1063/5.0219555.
- Vancouver
- 1.Cardona Sanchez D, Chatzakou M, Delgado J, Kumar V, Ruzhansky M. Anharmonic semigroups and applications to global well-posedness of nonlinear heat equations. JOURNAL OF MATHEMATICAL PHYSICS. 2025;66(8).
- IEEE
- [1]D. Cardona Sanchez, M. Chatzakou, J. Delgado, V. Kumar, and M. Ruzhansky, “Anharmonic semigroups and applications to global well-posedness of nonlinear heat equations,” JOURNAL OF MATHEMATICAL PHYSICS, vol. 66, no. 8, 2025.
@article{01KAKR6MCC6DGVAC43PBY035FY,
abstract = {{In this work we consider the semigroup e(k,& ell;)(-tA)(gamma) for gamma > 0 associated to an anharmonic oscillator of the form A(k,& ell;)=(-Delta)& ell;+|x|2k where k, & ell; are integers >= 1. By introducing a suitable H & ouml;rmander metric on the phase-space we analyze the semigroup e(-t)A(k,& ell;)(gamma) within the framework of Hormander S(M, g) classes and obtain mapping properties in the scale of modulation spaces M-p,M-q, 0 < p,q <= infinity 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 A(k,& ell;)(gamma) It is worth noting that the results presented in this paper are novel, even in the case where gamma = 1.}},
articleno = {{081509}},
author = {{Cardona Sanchez, Duvan and Chatzakou, Marianna and Delgado, Julio and Kumar, Vishvesh and Ruzhansky, Michael}},
issn = {{0022-2488}},
journal = {{JOURNAL OF MATHEMATICAL PHYSICS}},
keywords = {{PSEUDODIFFERENTIAL-OPERATORS,SPACES,BOUNDEDNESS,SCHRODINGER}},
language = {{eng}},
number = {{8}},
pages = {{21}},
title = {{Anharmonic semigroups and applications to global well-posedness of nonlinear heat equations}},
url = {{http://doi.org/10.1063/5.0219555}},
volume = {{66}},
year = {{2025}},
}
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