Nonexistence results for ultra-parabolic equations and systems involving fractional Laplacian operator in Heisenberg group

In this paper, sufficient conditions are obtained for the nonexistence of solutions to the Cauchy problems for ultra-parabolic equations involving fractional Laplacian operator. The nonexistence result is also extended to the corresponding system. The results to such problems are derived in the Heis...

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Autor principal: Tsegaw, Birilew Belayneh
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Elsevier 2022
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9568845/
https://www.ncbi.nlm.nih.gov/pubmed/36254281
http://dx.doi.org/10.1016/j.heliyon.2022.e10976
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author Tsegaw, Birilew Belayneh
author_facet Tsegaw, Birilew Belayneh
author_sort Tsegaw, Birilew Belayneh
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description In this paper, sufficient conditions are obtained for the nonexistence of solutions to the Cauchy problems for ultra-parabolic equations involving fractional Laplacian operator. The nonexistence result is also extended to the corresponding system. The results to such problems are derived in the Heisenberg group. The proofs of our nonexistence theorems are based on the nonlinear capacity method. This method is based on the choice of a suitable test function in the weak formulation of the considered problems.
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spelling pubmed-95688452022-10-16 Nonexistence results for ultra-parabolic equations and systems involving fractional Laplacian operator in Heisenberg group Tsegaw, Birilew Belayneh Heliyon Research Article In this paper, sufficient conditions are obtained for the nonexistence of solutions to the Cauchy problems for ultra-parabolic equations involving fractional Laplacian operator. The nonexistence result is also extended to the corresponding system. The results to such problems are derived in the Heisenberg group. The proofs of our nonexistence theorems are based on the nonlinear capacity method. This method is based on the choice of a suitable test function in the weak formulation of the considered problems. Elsevier 2022-10-10 /pmc/articles/PMC9568845/ /pubmed/36254281 http://dx.doi.org/10.1016/j.heliyon.2022.e10976 Text en © 2022 The Author(s) https://creativecommons.org/licenses/by-nc-nd/4.0/This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
spellingShingle Research Article
Tsegaw, Birilew Belayneh
Nonexistence results for ultra-parabolic equations and systems involving fractional Laplacian operator in Heisenberg group
title Nonexistence results for ultra-parabolic equations and systems involving fractional Laplacian operator in Heisenberg group
title_full Nonexistence results for ultra-parabolic equations and systems involving fractional Laplacian operator in Heisenberg group
title_fullStr Nonexistence results for ultra-parabolic equations and systems involving fractional Laplacian operator in Heisenberg group
title_full_unstemmed Nonexistence results for ultra-parabolic equations and systems involving fractional Laplacian operator in Heisenberg group
title_short Nonexistence results for ultra-parabolic equations and systems involving fractional Laplacian operator in Heisenberg group
title_sort nonexistence results for ultra-parabolic equations and systems involving fractional laplacian operator in heisenberg group
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9568845/
https://www.ncbi.nlm.nih.gov/pubmed/36254281
http://dx.doi.org/10.1016/j.heliyon.2022.e10976
work_keys_str_mv AT tsegawbirilewbelayneh nonexistenceresultsforultraparabolicequationsandsystemsinvolvingfractionallaplacianoperatorinheisenberggroup

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