کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4609321 1338506 2016 43 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Eventually and asymptotically positive semigroups on Banach lattices
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Eventually and asymptotically positive semigroups on Banach lattices
چکیده انگلیسی

We develop a theory of eventually positive C0C0-semigroups on Banach lattices, that is, of semigroups for which, for every positive initial value, the solution of the corresponding Cauchy problem becomes positive for large times. We give characterisations of such semigroups by means of spectral and resolvent properties of the corresponding generators, complementing existing results on spaces of continuous functions. This enables us to treat a range of new examples including the square of the Laplacian with Dirichlet boundary conditions, the bi-Laplacian on LpLp-spaces, the Dirichlet-to-Neumann operator on L2L2 and the Laplacian with non-local boundary conditions on L2L2 within the one unified theory. We also introduce and analyse a weaker notion of eventual positivity which we call “asymptotic positivity”, where trajectories associated with positive initial data converge to the positive cone in the Banach lattice as t→∞t→∞. This allows us to discuss further examples which do not fall within the above-mentioned framework, among them a network flow with non-positive mass transition and a certain delay differential equation.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 261, Issue 5, 5 September 2016, Pages 2607–2649
نویسندگان
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