@article{Choudhary2026, 
author = {Majid Ali Choudhary and Foued Aloui and Maged Z. Youssef and Mohammad Nazrul Islam Khan},
title = {Li–Yau gradient estimates of weighted nonlinear diffusion equations under geometric flow},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {6},
pages = {16008-16026},
keywords = {Harnack inequality, Li–Yau-type gradient estimate, geometric flow, partial differential equations, Ricci curvature},
url = {https://www.sciopen.com/article/10.3934/math.2026659},
doi = {10.3934/math.2026659},
abstract = {In the present study, we establish novel gradient bounds reminiscent of Li–Yau inequalities for strictly positive solutions of a specific category of weighted nonlinear diffusion equations incorporating a potential term, formulated as         ∂          t        u  (  z  ,  t  )  =      Δ          ϕ            u          p        (  z  ,  t  )  +  C      u          q        (  z  ,  t  )  ,    (  z  ,  t  )  ∈  M  ×  [  0  ,  T  ]  ,where the underlying space is a weighted Riemannian manifold    (      M    n    ,  g  (  t  )  ,      e          −      ϕ            d    v  ) evolving under a geometric flow governed by              ∂      g              ∂      t        =  2  h  (  t  ). As a direct consequence, we further establish associated Harnack-type inequalities for such evolving settings using partial differential equations.}
}