Results 11 to 20 of about 300 (51)
Tensor Product Technique and Atomic Solution of Fractional Partial Differential Equations
Journal of Applied MathematicsJEL Classification: 34G10 ...
Ma’mon Abu Hammad +3 more
doaj +2 more sources
On the decoupled Markov group conjecture
Bulletin of the London Mathematical Society, Volume 53, Issue 1, Page 240-247, February 2021., 2021 Abstract The Markov group conjecture, a long‐standing open problem in the theory of Markov processes with countable state space, asserts that a strongly continuous Markov semigroup T=(Tt)t∈[0,∞) on ℓ1 has bounded generator if the operator T1 is bijective. Attempts to disprove the conjecture have often aimed at glueing together finite‐dimensional matrix
Jochen Glück
wiley +1 more source
On almost automorphic solutions of linear operational‐differential equations
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 22, Page 1179-1182, 2004., 2004 We prove almost periodicity and almost automorphy of bounded solutions of linear differential equations x′(t) = Ax(t) + f(t) for some class of linear operators acting in a Banach space.
Gaston M. N′Guérékata
wiley +1 more source
Fragmentation arising from a distributional initial condition [PDF]
, 2010 A standard model for pure fragmentation is subjected to an initial condition of Dirac-delta type. Results for a corresponding abstract Cauchy problem are derived via the theory of equicontinuous semigroups of operators on locally convex spaces.
Aizenman +15 more
core +1 more source
On a higher‐order evolution equation with a Stepanov‐bounded solution
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 72, Page 3959-3964, 2004., 2004 We study strong solutions u : ℝ → X, a Banach space X, of the nth‐order evolution equation u(n) − Au(n−1) = f, an infinitesimal generator of a strongly continuous group A : D(A)⊆X → X, and a given forcing term f : ℝ → X. It is shown that if X is reflexive, u and u(n−1) are Stepanov‐bounded, and f is Stepanov almost periodic, then u and all derivatives ...
Aribindi Satyanarayan Rao
wiley +1 more source
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 45, Page 2401-2422, 2004., 2004 Necessary and sufficient conditions for a scalar type spectral operator in a Banach space to be a generator of an infinite differentiable or a Gevrey ultradifferentiable C0‐semigroup are found, the latter formulated exclusively in terms of the operator′s spectrum.
Marat V. Markin
wiley +1 more source
Quantified versions of Ingham's theorem [PDF]
, 2015 We obtain quantified versions of Ingham's classical Tauberian theorem and some of its variants by means of a natural modification of Ingham's own simple proof.
Chill, Ralph, Seifert, David
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The fundamental solutions for fractional evolution equations of parabolic type
International Journal of Stochastic Analysis, Volume 2004, Issue 3, Page 197-211, 2004., 2004 The fundamental solutions for linear fractional evolution equations are obtained. The coefficients of these equations are a family of linear closed operators in the Banach space. Also, the continuous dependence of solutions on the initial conditions is studied. A mixed problem of general parabolic partial differential equations with fractional order is
Mahmoud M. El-Borai
wiley +1 more source
Hyperbolic differential‐operator equations on a whole axis
Abstract and Applied Analysis, Volume 2004, Issue 2, Page 99-113, 2004., 2004 We give an abstract interpretation of initial boundary value problems for hyperbolic equations such that a part of initial boundary value conditions contains also a differentiation on the time t of the same order as equations. The case of stable solutions of abstract hyperbolic equations is treated.
Yakov Yakubov
wiley +1 more source
Open Mathematics, 2019 It is shown that, if all weak solutions of the evolution ...
Markin Marat V.
doaj +1 more source