| 一类发展的p(x)-Laplace方程解的存在唯一性 |
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| 引用本文： | 曾羽群.一类发展的p(x)-Laplace方程解的存在唯一性[J].集美大学学报(自然科学版),2021,26(2):119-124. |
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| 作者姓名： | 曾羽群 |
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| 作者单位： | (集美大学理学院,福建 厦门 361021) |
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| 摘 要： | 讨论一类发展的p(x)-Laplace方程ut=div(a(x,t)∣△u∣p(x)－2△u)+f(u,x,t)解的存在唯一性。不同于此前的研究，文中假设a(x,t)≥0，且当x∈Ω时，a(x,t)>0,解的稳定性是建立在一个合理的部分边界条件u(x,t)=0,(x,t)∈Σ1上，其中Σ1 Ω（0,T)仅仅是一个子流形。
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| 关 键 词： | 发展的p(x)-Laplace方程 存在唯一性 稳定性 部分边界条件 子流形 |
Existence and Uniqueness of Solutions to an Evolutionary p(x) -Laplace Equation |
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| ZENG Yuqun.Existence and Uniqueness of Solutions to an Evolutionary p(x) -Laplace Equation[J].the Editorial Board of Jimei University(Natural Science),2021,26(2):119-124. |
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| Authors: | ZENG Yuqun |
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| Affiliation: | (School of Science,Jimei University,Xiamen 361021,China) |
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| Abstract: | The following evolutionary p(x)-Laplace equations t=div(a(x,t)∣△u∣p(x)－2△u)+f(u,x,t) were discussed,and the existence and the uniqueness of weak solutions were proved.Different from the previous works,it was assumed a(x,t)≥0and a(x,t)x∈Ω>0 in this paper.The stability of weak solutions was based on a reasonable partial boundary value condition u(x,t)=0,(x,t)∈Σ1,where Σ1Ω×(0,T) was just a submanifold. |
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| Keywords: | evolutionary p(x)-Laplace equation existence and uniqueness stability partial boundary value condition submanifold |
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