Opuscula Math. 44, no. 4 (2024), 587-623

Opuscula Mathematica

On the solvability of some parabolic equations involving nonlinear boundary conditions with L1 data

Laila Taourirte
Abderrahim Charkaoui
Nour Eddine Alaa

Abstract. We analyze the existence of solutions for a class of quasilinear parabolic equations with critical growth nonlinearities, nonlinear boundary conditions, and \(L^1\) data. We formulate our problems in an abstract form, then using some techniques of functional analysis, such as Leray-Schauder's topological degree associated with the truncation method and very interesting compactness results, we establish the existence of weak solutions to the proposed models.

Keywords: quasilinear parabolic equation, nonlinear boundary conditions, weak solutions, Leray-Schauder topological degree, \(L^1\)-data.

Mathematics Subject Classification: 35K59, 35K55, 35A01, 35B09, 35D30.

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  • Abderrahim Charkaoui
  • ORCID iD https://orcid.org/0000-0003-1425-7248
  • Interdisciplinary Research Laboratory in Sciences, Education and Training, Higher School of Education and Training of Berrechid (ESEFB), Hassan First University, Morocco
  • Nour Eddine Alaa (corresponding author)
  • ORCID iD https://orcid.org/0000-0001-8169-8663
  • Laboratory LAMAI, Faculty of Science and Technology of Marrakech, B.P. 549, Av. Abdelkarim Elkhattabi, 40000, Marrakech, Morocco
  • Communicated by Patrizia Pucci.
  • Received: 2023-04-12.
  • Revised: 2024-01-30.
  • Accepted: 2024-01-31.
  • Published online: 2024-04-29.
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Cite this article as:
Laila Taourirte, Abderrahim Charkaoui, Nour Eddine Alaa, On the solvability of some parabolic equations involving nonlinear boundary conditions with L1 data, Opuscula Math. 44, no. 4 (2024), 587-623, https://doi.org/10.7494/OpMath.2024.44.4.587

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