Generalized Young Measure Solutions for a Class of Quasilinear Parabolic Equations with Linear Growth
Analysis of PDEs
2024-06-04 v1
Abstract
Using the generalized Young measure theory, we extend the theory of Young measure solutions to a class of quasilinear parabolic equations with linear growth, and introduce the concept of generalized Young measure solutions. We prove the existence and uniqueness of the generalized Young measure solutions. In addition, for the gradient flow of convex parabolic variational integral, we show that the generalized Young measure solutions are equivalent to the strong solutions.
Keywords
Cite
@article{arxiv.2406.01043,
title = {Generalized Young Measure Solutions for a Class of Quasilinear Parabolic Equations with Linear Growth},
author = {Jingfeng Shao and Zhichang Guo and Chao Zhang},
journal= {arXiv preprint arXiv:2406.01043},
year = {2024}
}
Comments
This paper extend the theory of Young measure solutions to a class of quasilinear parabolic equations with linear growth, and introduce a concept of generalized Young measure solutions