On the assumption that the Cauchy problem for incomplete second order abstract differential equation (u″(t)=Au(t), -∞ <t <∞) is well posed and the Cauchy problem for complete second order abstract diff...On the assumption that the Cauchy problem for incomplete second order abstract differential equation (u″(t)=Au(t), -∞ <t <∞) is well posed and the Cauchy problem for complete second order abstract differential equation ( u″(t)+A 1u′(t)+A 0u(t)=0, t≥0 ) is strongly well posed, the necessary conditions for their solutions to be pseudo almost periodic are derived.展开更多
In this paper, the integral problem for linear and nonlinear wave equations is studied. The equation involves abstract operator A in Hilbert space H. Here, assuming enough smoothness on the initial data and the operat...In this paper, the integral problem for linear and nonlinear wave equations is studied. The equation involves abstract operator A in Hilbert space H. Here, assuming enough smoothness on the initial data and the operators, the existence, uniqueness, regularity properties of solutions are established. By choosing the space H and A, the regularity properties of solutions of a wide class of wave equations in the field of physics are obtained.展开更多
In this paper,we consider an abstract third-order differential equation and deduce some results on the maximal regularity of its strict solution.We assume that the inhomogeneity appearing in the right-hand term of thi...In this paper,we consider an abstract third-order differential equation and deduce some results on the maximal regularity of its strict solution.We assume that the inhomogeneity appearing in the right-hand term of this equation belongs to some anistropic Holder spaces.We illustrate our results by a BVP involving a 3D Laplacian posed in a cusp domain of R^(4).展开更多
Some properties of integrated bisemigroup S(t) of linear operators on a Banach space X are studied. The structure of the positive and negative subspaces and the operation of integrated bisemigroup on corresponding dif...Some properties of integrated bisemigroup S(t) of linear operators on a Banach space X are studied. The structure of the positive and negative subspaces and the operation of integrated bisemigroup on corresponding differentiable subspace C-n are established. respectively. The decomposition of the infinitesimal generator A of S(t) and other interested problems are also considered. As application, an abstract boundary value problem is discussed.展开更多
文摘On the assumption that the Cauchy problem for incomplete second order abstract differential equation (u″(t)=Au(t), -∞ <t <∞) is well posed and the Cauchy problem for complete second order abstract differential equation ( u″(t)+A 1u′(t)+A 0u(t)=0, t≥0 ) is strongly well posed, the necessary conditions for their solutions to be pseudo almost periodic are derived.
文摘In this paper, the integral problem for linear and nonlinear wave equations is studied. The equation involves abstract operator A in Hilbert space H. Here, assuming enough smoothness on the initial data and the operators, the existence, uniqueness, regularity properties of solutions are established. By choosing the space H and A, the regularity properties of solutions of a wide class of wave equations in the field of physics are obtained.
文摘In this paper,we consider an abstract third-order differential equation and deduce some results on the maximal regularity of its strict solution.We assume that the inhomogeneity appearing in the right-hand term of this equation belongs to some anistropic Holder spaces.We illustrate our results by a BVP involving a 3D Laplacian posed in a cusp domain of R^(4).
基金the National Key Project of China the Natural Science Foundation of Shanxi
文摘Some properties of integrated bisemigroup S(t) of linear operators on a Banach space X are studied. The structure of the positive and negative subspaces and the operation of integrated bisemigroup on corresponding differentiable subspace C-n are established. respectively. The decomposition of the infinitesimal generator A of S(t) and other interested problems are also considered. As application, an abstract boundary value problem is discussed.
