Gradient Estimates and Harnack Inequalities of a Nonlinear Heat Equation for the Finsler-Laplacian
DOI:
https://doi.org/10.15407/mag17.04.521Анотація
Нехай $(M^{n}, F, m)$ є $n$-вимiрним компактним фiнслеровим многовидом. У цiй роботi ми вивчаємо нелiнiйне рiвняння теплопровiдностi
$$ \partial_{t}u=\Delta_{m} u\quad\text{on}\ M^n\times[0, T], $$
де $\Delta_{m}$ є фiнслеровим лапласiаном. Одержано градiєнтнi оцiнки типу Лi–Яу для позитивних глобальних розв’язкiв цього рiвняння на статичних фiнслерових многовидах, а також пiд дiєю потоку Фiнслера–Рiччi. Як наслiдок, в обох випадках також одержано вiдповiднi нерiвностi Гарнака.
Mathematics Subject Classification: 35K55, 53C21
Ключові слова:
градiєнтнi оцiнки Лi–Яу, нерiвнiсть Гарнака, нелiнiйне рiвняння теплопровiдностi, потiк Фiнслера–РiччiПосилання
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