Hasna Moujani, Abderrazak Kassidi, Ali El Mfadel
Abstract:
This article explores the existence of weak solutions to a parabolic problem governed by
the \(\tau\)-Laplacian-like operator \(-\Delta_{\tau}^\ell \delta \) and a nonlinear source
term \(\eta \text{ div }\phi(y, t, \delta)\). Under suitable growth conditions on the
nonlinear function \(\phi\), we ensure that the weak formulation of the problem is well-
posed, leading to the existence result. This result is obtained through the application
of Galerkin's approximation technique to build approximate solutions, as well as
the Young measures theory, which provides a framework for handling the complexities
introduced by the nonlinearity.
Submitted February 3, 2026. Published May 12, 2026.
Math Subject Classifications: 26A33, 37C75, 34A08, 93D40.
Key Words: Parabolic problem; weak solution; \(\tau\)-Laplacian-like operators;
Young measure; Galerkin approximation.
DOI: 10.58997/ejde.2026.35
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| Hasna Moujani Sultan Moulay Slimane University Laboratory of Applied Mathematics and Scientific Computing Beni Mellal, Morocco email: hasnaemoujani@gmail.com |
| Abderrazak Kassidi Sultan Moulay Slimane University Laboratory of Applied Mathematics and Scientific Computing Beni Mellal, Morocco email: a.kassidi@usms.ma |
| Ali El Mfadel Sultan Moulay Slimane University Laboratory of Applied Mathematics and Scientific Computing Beni Mellal, Morocco email: a.elmfadel@usms.ma |
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