TY  - JOUR
ID  - Taourirte2024
LB  - Taourirte2024
AU  - Taourirte, Laila
AU  - Charkaoui, Abderrahim
AU  - Alaa, Nour Eddine
TI  - On the solvability of some parabolic equations involving nonlinear boundary conditions with L<sup>1</sup> data
ST  - On the solvability of some parabolic equations involving nonlinear boundary conditions with L<sup>1</sup> data
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2024
VL  - 44
IS  - 4
SP  - 587
EP  - 623
DO  - https://doi.org/10.7494/OpMath.2024.44.4.587
UR  - https://doi.org/10.7494/OpMath.2024.44.4.587
AB  - 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.
KW  - quasilinear parabolic equation
KW  - nonlinear boundary conditions
KW  - weak solutions
KW  - Leray-Schauder topological degree
KW  - \(L^1\)-data
SN  - 1232-9274
ER  -