In this paper, we consider the time‐fractional order Schrödinger equation that is a fundamental equation in fractional quantum mechanics. By using the spectral theorem, we prove Duhamel''s formula and give some properties of solution operators, which can be used to study the local existence ...
In Proposition 2, equation (6) is of course just the Duhamel formula from analytic semigroup theory. However, since X also contains non-classical solutions, (6) requires a proof in the present context-but as noted, it suffices just to reinforce the classical argument by the injectivity of ...
In this paper,the piecewise Birkhoff interpolating polynomial was employed to approximate arbitrary dynamic loads in the Duhamel integral for the solution of dynamic response,and the relative formulae are derived. 在求解动力响应的Duhamel积分中 ,利用分段Birkhoff插值多项式逼近任意动力荷载 ,并推导了相关公...
In this paper, we consider the time-fractional order Schrodinger equation that is a fundamental equation in fractional quantum mechanics. By using the spectral theorem, we prove Duhamel's formula and give some properties of solution operators, which can be used to study the local existence and ...
No Abstract available for this article.doi:10.1007/BF01200374Rhoda J. HughesBirkhäuser-VerlagIntegral Equations and Operator Theory
Duhamel's theorem based solution method is only valid for linear cases [ 2 ], as it can be considered to be a result of the superposition principle application. This chapter contains formula derivations for Duhamel integral for continuous boundary condition function and also the one having some ...
The solution of heat equation inside oscillating gas bubble with moving boundary was obtained by Fourier's method. The integral formula for interface heat flux, containing theta-function in the integrand was derived. The kernel of the integral is represented by a series of exponential functions, ...
The paper considers the initial boundary value problem for the wave equation for the case of three spatial variables. The definition of a generalized solution has been introduced and the theorem of unique existence has been proved. A new formula was proposed, being an analog of the well-known ...
The Duhamel product of functions f and g is defined by the formula (f * g)(x) = d/(dx) ∫_0~x f(x-t)g(t)dt. In the present paper, the Duhamel product is used in the study of spectral multiplicity for direct sums of operators and in the description of cyclic vectors of the...