当前位置: X-MOL 学术J. Evol. Equ. › 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.)
Convex semigroups on $$L^p$$ L p -like spaces
Journal of Evolution Equations ( IF 1.4 ) Pub Date : 2021-04-08 , DOI: 10.1007/s00028-021-00693-3
Robert Denk , Michael Kupper , Max Nendel

In this paper, we investigate convex semigroups on Banach lattices with order continuous norm, having \(L^p\)-spaces in mind as a typical application. We show that the basic results from linear \(C_0\)-semigroup theory extend to the convex case. We prove that the generator of a convex \(C_0\)-semigroup is closed and uniquely determines the semigroup whenever the domain is dense. Moreover, the domain of the generator is invariant under the semigroup, a result that leads to the well-posedness of the related Cauchy problem. In a last step, we provide conditions for the existence and strong continuity of semigroup envelopes for families of \(C_0\)-semigroups. The results are discussed in several examples such as semilinear heat equations and nonlinear integro-differential equations.



中文翻译:

类$$$ ^^ $$$ L p上的凸半群

在本文中,我们研究了具有连续连续范数的Banach格上的凸半群,并以\(L ^ p \)-空间为典型应用。我们证明了线性\(C_0 \)-半群理论的基本结果扩展到凸情况。我们证明了凸\(C_0 \)-半群的生成器是封闭的,并且每当域为稠密时才唯一地确定半群。此外,生成器的域在半群下是不变的,其结果导致相关柯西问题的适定性。在最后一步中,我们为\(C_0 \)族的半群信封的存在和强连续性提供了条件。-半组。在几个示例中讨论了结果,例如半线性热方程和非线性积分微分方程。

更新日期:2021-04-09
down
wechat
bug