Dichotomy and Fredholm Properties of Evolution Equations
نویسندگان
چکیده
Under minimal assumptions, we characterize the Fredholmity and compute the Fredholm index of abstract differential operators −d/dt + A(·) acting on spaces of functions f : R → X. Here A(t) are (in general) unbounded operators on the Banach space X and our results are formulated in terms of exponential dichotomies on two halflines for the propagtor solving the evolution equation u̇(t) = A(t)u(t) in a mild sense.
منابع مشابه
The combined reproducing kernel method and Taylor series for solving nonlinear Volterra-Fredholm integro-differential equations
In this letter, the numerical scheme of nonlinear Volterra-Fredholm integro-differential equations is proposed in a reproducing kernel Hilbert space (RKHS). The method is constructed based on the reproducing kernel properties in which the initial condition of the problem is satised. The nonlinear terms are replaced by its Taylor series. In this technique, the nonlinear Volterra-Fredholm integro...
متن کاملNumerical solution of Fredholm integral-differential equations on unbounded domain
In this study, a new and efficient approach is presented for numerical solution of Fredholm integro-differential equations (FIDEs) of the second kind on unbounded domain with degenerate kernel based on operational matrices with respect to generalized Laguerre polynomials(GLPs). Properties of these polynomials and operational matrices of integration, differentiation are introduced and are ultili...
متن کاملA Numerical Approach for Solving of Two-Dimensional Linear Fredholm Integral Equations with Boubaker Polynomial Bases
In this paper, a new collocation method, which is based on Boubaker polynomials, is introduced for the approximate solutions of a class of two-dimensional linear Fredholm integral equationsof the second kind. The properties of two-dimensional Boubaker functions are presented. The fundamental matrices of integration with the collocation points are utilized to reduce the solution of the integral ...
متن کاملThe Dichotomy Theorem for evolution bi-families ?
We prove that the operator G, the closure of the first-order differential operator −d/dt + D(t) on L2(R, X), is Fredholm if and only if the not well-posed equation u′(t) = D(t)u(t), t ∈ R, has exponential dichotomies on R+ and R− and the ranges of the dichotomy projections form a Fredholm pair; moreover, the index of this pair is equal to the Fredholm index of G. Here X is a Hilbert space, D(t)...
متن کاملA computational wavelet method for numerical solution of stochastic Volterra-Fredholm integral equations
A Legendre wavelet method is presented for numerical solutions of stochastic Volterra-Fredholm integral equations. The main characteristic of the proposed method is that it reduces stochastic Volterra-Fredholm integral equations into a linear system of equations. Convergence and error analysis of the Legendre wavelets basis are investigated. The efficiency and accuracy of the proposed method wa...
متن کامل