Renormalized Solution for the Nonlinear Parabolic Problem with Lower Order Terms

Shijun Li; Boai Huang; Shaopeng Xu

Renormalized Solution for the Nonlinear Parabolic Problem with Lower Order Terms

Analysis of PDEs 2026-05-07 v1

Authors: Shijun Li , Boai Huang , Shaopeng Xu

Abstract

In this paper, we consider the following problem: $\begin{cases} -\nabla\cdot A(x,u,\nabla u) + H(x,u,\nabla u) = f(x), & x \in \Omega, u = 0, & x \in \partial \Omega, \end{cases}$ in a bounded open set $\Omega \subset \mathbb{R}^N$ . We have established certain gradient estimates and proved the existence of a renormalized solution for the equation.

Keywords

parabolic equations

Cite

@article{arxiv.2605.04820,
  title  = {Renormalized Solution for the Nonlinear Parabolic Problem with Lower Order Terms},
  author = {Shijun Li and Boai Huang and Shaopeng Xu},
  journal= {arXiv preprint arXiv:2605.04820},
  year   = {2026}
}

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