当前位置: X-MOL 学术Rev. Math. Phys. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Asymptotic to systems with memory and non-local initial data
Reviews in Mathematical Physics ( IF 1.4 ) Pub Date : 2019-10-30 , DOI: 10.1142/s0129055x20500142
Jaime E. Muñoz Rivera 1 , Verónica Poblete 2 , Juan C. Pozo 3 , Octavio Vera 4
Affiliation  

We study the existence and the asymptotic behavior of the solution of an abstract viscoelastic system submitted to non-local initial data. [Formula: see text] [Formula: see text] where [Formula: see text] and [Formula: see text] are differential operators satisfying [Formula: see text] for [Formula: see text]. We prove that the model is well-posed. Concerning the asymptotic behavior, we show that the exponential decay holds if and only if [Formula: see text] and [Formula: see text] goes to zero exponentially. Otherwise if [Formula: see text] or the kernel goes to zero polynomially, then the solution only decays polynomially. We show the optimality of our result. Finally, we consider the non-dissipative case.

中文翻译:

对具有内存和非本地初始数据的系统渐近

我们研究了提交给非局部初始数据的抽象粘弹性系统解的存在性和渐近行为。[公式:见正文] [公式:见正文] 其中[公式:见正文]和[公式:见正文]是满足[公式:见正文]的[公式:见正文]的微分算子。我们证明了该模型是适定的。关于渐近行为,我们表明当且仅当 [公式:参见文本] 和 [公式:参见文本] 以指数方式变为零时,指数衰减成立。否则,如果 [公式:参见文本] 或内核多项式归零,则解只会多项式衰减。我们展示了我们的结果的最优性。最后,我们考虑非耗散的情况。
更新日期:2019-10-30
down
wechat
bug