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A generation theorem for the perturbation of exponentially equicontinuous C₀-semigroups on locally convex spaces | ||
| Journal of Mathematics and Modeling in Finance | ||
| دوره 5، شماره 1، مهر 2025، صفحه 167-173 اصل مقاله (188.3 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22054/jmmf.2025.85197.1173 | ||
| نویسنده | ||
| Jawad Ettayb* | ||
| Regional Academy of Education and Training, Casablanca-Settat, Morocco | ||
| چکیده | ||
| In this paper, we study the well-posedness of the evolution equation of the form u'(t) = Au(t) + Cu(t), t ≥ 0 where A is the infinitesimal generator of an exponentially equicontinuous C₀-semigroup and C is a (possibly unbounded) linear operator in a sequentially complete locally convex Hausdorff space X. In particular, we demonstrate that if A generates an exponentially equicontinuous C₀-semigroup (T_A(t))_{t ≥ 0} satisfying p(T_A(t)x) ≤ e^{ωt}q(x) and C is a linear operator on X such that D(A) ⊂ D(C) and {K⁻¹(μ-ω)ⁿ(CR(μ, A))ⁿ; μ > ω, n ∈ ℕ} is equicontinuous, then the above-mentioned evolution equation is well-posed, that is, A + C generates an exponentially equicontinuous C₀-semigroup (T_{A+C}(t))_{t ≥ 0} satisfying p(T_{A+C}(t)x) ≤ e^{(ω+K)t}q(x). | ||
| کلیدواژهها | ||
| C₀-semigroups؛ continuous linear operators؛ locally convex spaces | ||
| مراجع | ||
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