Nonlinear parabolic equations with Laplacian-like operators and Young measures

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. For more information and the latex files, see https://ejde.math.txstate.edu/Volumes/2026/35/abstr.html