Results 21 to 30 of about 55 (54)
Linear neutral partial differential equations: a semigroup approach
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 23, Page 1433-1445, 2003., 2003 We study linear neutral PDEs of the form (∂/∂t)Fut = BFut + Φut, t ≥ 0; u0(t) = φ(t), t ≤ 0, where the function u(⋅) takes values in a Banach space X. Under appropriate conditions on the difference operator F and the delay operator Φ, we construct a C0‐semigroup on C0(ℝ−, X) yielding the solutions of the equation.
Rainer Nagel, Nguyen Thieu Huy
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Existence of the Conformable Double Laplace–Elzaki Transform and Applications
Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.In this study, we introduce and establish the existence of the conformable fractional Laplace–Elzaki transform (CLET), a new integral transform designed to handle fractional‐order problems. Several fundamental properties and theorems of the CLET are derived and discussed.
Zaid Zaqzaq +3 more
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On the mild solutions of higher‐order differential equations in Banach spaces
Abstract and Applied Analysis, Volume 2003, Issue 15, Page 865-880, 2003., 2003 For the higher‐order abstract differential equation u(n)(t) = Au(t) + f(t), t ∈ ℝ, we give a new definition of mild solutions. We then characterize the regular admissibility of a translation‐invariant subspace ℳ of BUC(ℝ, E) with respect to the above‐mentioned equation in terms of solvability of the operator equation AX − X𝒟n = C.
Nguyen Thanh Lan
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Abstract Cauchy Problem of Conformable Type and Operator Ideals in Hilbert Space
Journal of Function Spaces, Volume 2025, Issue 1, 2025.In this paper, we focus our study on the fractional homogeneous abstract Cauchy problems of conformable type, wβ(t) = Uw(t), t ∈ [0, T), T ≤ ∞, w(0) = x, where U is a linear operator that generates a fractional β‐semigroup on a Hilbert space H. In fact, we gave an answer to the question if U is the infinitesimal generator of a conformable β‐semigroup ...
Sharifa Al−Sharif +3 more
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Large diffusivity finite‐dimensional asymptotic behaviour of a semilinear wave equation
Journal of Applied Mathematics, Volume 2003, Issue 8, Page 409-427, 2003., 2003 We study the effects of large diffusivity in all parts of the domain in a linearly damped wave equation subject to standard zero Robin‐type boundary conditions. In the linear case, we show in a given sense that the asymptotic behaviour of solutions verifies a second‐order ordinary differential equation.
Robert Willie
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Journal of Mathematics, Volume 2025, Issue 1, 2025.This paper investigates an abstract nonhomogeneous backward Cauchy problem governed by an unbounded linear operator in a Hilbert space H. The coefficient operator in the equation is assumed to be unbounded, self‐adjoint, positive, and to possess a discrete spectrum, with data prescribed at the final time t = T.
Nihed Teniou, Xian-Ming Gu
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International Journal of Mathematics and Mathematical Sciences, Volume 32, Issue 9, Page 573-578, 2002., 2002 In a Banach space, if u is a Stepanov almost periodic solution of a certain nth‐order infinitesimal generator and time‐dependent operator differential equation with a Stepanov almost periodic forcing function, then u, u′, …, u (n−2) are all strongly almost periodic and u (n−1) is weakly almost periodic.
Aribindi Satyanarayan Rao
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A note on the spectral operators of scalar type and semigroups of bounded linear operators
International Journal of Mathematics and Mathematical Sciences, Volume 32, Issue 10, Page 635-640, 2002., 2002 It is shown that, for the spectral operators of scalar type, the well‐known characterizations of the generation of C0‐ and analytic semigroups of bounded linear operators can be reformulated exclusively in terms of the spectrum of such operators, the conditions on the resolvent of the generator being automatically met and the corresponding semigroup ...
Marat V. Markin
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Abstract fractional integro-differential equations involving nonlocal initial conditions in
Advances in Difference Equations, 2011 In the present paper, we deal with the Cauchy problems of abstract fractional integro-differential equations involving nonlocal initial conditions in α-norm, where the operator A in the linear part is the generator of a compact analytic semigroup ...
Wang Rong-Nian, Liu Jun, Chen De-Han
doaj
Regulatory modules mediating the complex neural expression patterns of the homeobrain gene during Drosophila brain development. [PDF]
Hereditas, 2022 Hildebrandt K +8 more
europepmc +1 more source