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The heat equation with singular potentials : II. hypoelliptic case

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Abstract
In this paper we consider the heat equation with a strongly singular potential and show that it has a very weak solution. Our analysis is devoted to general hypoelliptic operators and is developed in the setting of graded Lie groups. The current work continues and extends the work (Altybay et al. in Appl. Math. Comput. 399:126006, 2021), where the classical heat equation on the Euclidean space was considered.
Keywords
Heat equation, Rockland operator, Cauchy problem, Graded Lie group, Weak solution, Singular mass, Very weak solution, Regularisation

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MLA
Chatzakou, Marianna, et al. “The Heat Equation with Singular Potentials : II. Hypoelliptic Case.” ACTA APPLICANDAE MATHEMATICAE, vol. 179, no. 1, 2022, doi:10.1007/s10440-022-00487-w.
APA
Chatzakou, M., Ruzhansky, M., & Tokmagambetov, N. (2022). The heat equation with singular potentials : II. hypoelliptic case. ACTA APPLICANDAE MATHEMATICAE, 179(1). https://doi.org/10.1007/s10440-022-00487-w
Chicago author-date
Chatzakou, Marianna, Michael Ruzhansky, and Niyaz Tokmagambetov. 2022. “The Heat Equation with Singular Potentials : II. Hypoelliptic Case.” ACTA APPLICANDAE MATHEMATICAE 179 (1). https://doi.org/10.1007/s10440-022-00487-w.
Chicago author-date (all authors)
Chatzakou, Marianna, Michael Ruzhansky, and Niyaz Tokmagambetov. 2022. “The Heat Equation with Singular Potentials : II. Hypoelliptic Case.” ACTA APPLICANDAE MATHEMATICAE 179 (1). doi:10.1007/s10440-022-00487-w.
Vancouver
1.
Chatzakou M, Ruzhansky M, Tokmagambetov N. The heat equation with singular potentials : II. hypoelliptic case. ACTA APPLICANDAE MATHEMATICAE. 2022;179(1).
IEEE
[1]
M. Chatzakou, M. Ruzhansky, and N. Tokmagambetov, “The heat equation with singular potentials : II. hypoelliptic case,” ACTA APPLICANDAE MATHEMATICAE, vol. 179, no. 1, 2022.
@article{8754711,
  abstract     = {{In this paper we consider the heat equation with a strongly singular potential and show that it has a very weak solution. Our analysis is devoted to general hypoelliptic operators and is developed in the setting of graded Lie groups. The current work continues and extends the work (Altybay et al. in Appl. Math. Comput. 399:126006, 2021), where the classical heat equation on the Euclidean space was considered.}},
  articleno    = {{2}},
  author       = {{Chatzakou, Marianna and Ruzhansky, Michael and Tokmagambetov, Niyaz}},
  issn         = {{0167-8019}},
  journal      = {{ACTA APPLICANDAE MATHEMATICAE}},
  keywords     = {{Heat equation,Rockland operator,Cauchy problem,Graded Lie group,Weak solution,Singular mass,Very weak solution,Regularisation}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{20}},
  title        = {{The heat equation with singular potentials : II. hypoelliptic case}},
  url          = {{http://dx.doi.org/10.1007/s10440-022-00487-w}},
  volume       = {{179}},
  year         = {{2022}},
}

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