In this paper,we discuss on the convergence and approximation of an α times integrated semigroups. The Trotter kato theorems for an α times integrated semigroups are obtained.
The α-times integrated C semigroups, α > 0, are introduced and analyzed. The Laplace inverse transformation for α-times integrated C semigroups is obtained, some known results are generalized.
We establish some left and right multiplicative perturbations of a local α-timesintegrated C-semigroup S（·） on a complex Banach space X with non-densely defined genera- tor, which can be applied to obtain some...We establish some left and right multiplicative perturbations of a local α-timesintegrated C-semigroup S（·） on a complex Banach space X with non-densely defined genera- tor, which can be applied to obtain some additive perturbation results concerning S（·）. Some growth conditions of the perturbations of S（·） are also established.展开更多
The infinite generator of α-times Integrated C semigroups and the properties of resolvent are given. At the same time, we discuss the relationship between the existence of strong solution of a class of nonhomogeneous...The infinite generator of α-times Integrated C semigroups and the properties of resolvent are given. At the same time, we discuss the relationship between the existence of strong solution of a class of nonhomogeneous abstract Cauchy problem and α-times integrated C semigroups, and a sufficient and necessary condition is obtained.展开更多
In this paper, based on the theories of α-times Integrated Cosine Function, we discuss the approximation theorem for α-times Integrated Cosine Function and conclude the approximation theorem of exponentially bounded...In this paper, based on the theories of α-times Integrated Cosine Function, we discuss the approximation theorem for α-times Integrated Cosine Function and conclude the approximation theorem of exponentially bounded α-times Integrated Cosine Function by the approximation theorem of n-times integrated semigroups. If the semigroups are equicontinuous at each point ? , we give different methods to prove the theorem.展开更多
In this paper, by Laplace transform version of the Trotter-Kato approximation theorem and the integrated C-semigroup introduced by Myadera, the authors obtained some Trotter-Kato approximation theorems on exponentiall...In this paper, by Laplace transform version of the Trotter-Kato approximation theorem and the integrated C-semigroup introduced by Myadera, the authors obtained some Trotter-Kato approximation theorems on exponentially bounded C-semigroups, where the range of C (and so the domain of the generator) may not be dense. The authors deduced the corresponding results on exponentially bounded integrated semigroups with nondensely generators. The results of this paper extended and perfected the results given by Lizama, Park and Zheng.展开更多
Integrated semigroups which are not exponentially bounded have been studied. The integrated solutions of inhomogeneous and nonlinear abstract Caucby problems are discussed. The reults extends and improves the theorems...Integrated semigroups which are not exponentially bounded have been studied. The integrated solutions of inhomogeneous and nonlinear abstract Caucby problems are discussed. The reults extends and improves the theorems in [1].展开更多
We introduce the notion of the contraction integrated semigroups and give the Lumber-Phillips characterization of the generator, and also the charaterazied generators of isometric integrated semigroups. For their appl...We introduce the notion of the contraction integrated semigroups and give the Lumber-Phillips characterization of the generator, and also the charaterazied generators of isometric integrated semigroups. For their application, a necessary and sufficient condition for q-matrices Q generating a contraction integrated semigroup is given, and a necessary and sufficient condition for a transition function to be a Feller-Reuter-Riley transition function is also given in terms of its q-matrix.展开更多
Let T be a singular integral operator bounded on Lp(Rn) for some p, 1 < p < ∞. The authors give a sufficient condition on the kernel of T so that when b ∈BMO, the commutator [b,T](f) = T(bf) - bT(f) is bounded...Let T be a singular integral operator bounded on Lp(Rn) for some p, 1 < p < ∞. The authors give a sufficient condition on the kernel of T so that when b ∈BMO, the commutator [b,T](f) = T(bf) - bT(f) is bounded on the space Lp for all p, 1 < p < ∞. The condition of this paper is weaker than the usual pointwise Hormander condition.展开更多
This paper is concerned with applications of integrated semigroups tothe following Cauchy problem:（ACP<sub>n</sub>） x<sup>n</sup>（t）=sum from i=0 to n-1 B<sub>i</sub>x<sup>...This paper is concerned with applications of integrated semigroups tothe following Cauchy problem:（ACP<sub>n</sub>） x<sup>n</sup>（t）=sum from i=0 to n-1 B<sub>i</sub>x<sup>i</sup>（t）,x<sup>i</sup>（0）=x<sub>i</sub>,0（?）i（?）n-1where B<sub>i</sub> （0（?）i（?）n-1） are closed linear operators on a Banach space X.Auniqueness theorem,a condition of the solvability,a condition of the exponentialwell-posedness,and some results for the special case that B<sub>n-1</sub> is bounded andD(B<sub>n-2</sub>)（?）D（B<sub>i</sub>）（0（?）i（?）n-3） are obtained.展开更多
A well-known result established by Arendt in 1987 with regard to the Laplace transforms in Banach spaces is developed. A Widder-Arendt theorem in the setting of sequentially complete locally convex spaces is set up (T...A well-known result established by Arendt in 1987 with regard to the Laplace transforms in Banach spaces is developed. A Widder-Arendt theorem in the setting of sequentially complete locally convex spaces is set up (Theorem 1.1). Moreover, integrated semigroups in such spaces are introduced and generation theorems and some basic properties for semigroups of this type are obtained. As examples, elliptic differential operators on certain classes of function spaces with locally convex topology are shown to be the generators of integrated semigroups under some conditions.展开更多
Let L be the infinitesimal generator of an analytic semigroup on L;（R;）with pointwise upper bounds on heat kernel,and denote by L;the fractional integrals of L.For a BMO function b（x）,we show a weak type Llog L es...Let L be the infinitesimal generator of an analytic semigroup on L;（R;）with pointwise upper bounds on heat kernel,and denote by L;the fractional integrals of L.For a BMO function b（x）,we show a weak type Llog L estimate of the commutators [b,L;]（f）(x) = b（x）L;（f）(x)-L;（bf）(x).We give applications to large classes of differential operators such as the Schr¨odinger operators and second-order elliptic operators of divergence form.展开更多
In this note, we investigated existence and uniqueness of entropy solution for triply nonlinear degenerate parabolic problem with zero-flux boundary condition. Accordingly to the case of doubly nonlinear degenerate pa...In this note, we investigated existence and uniqueness of entropy solution for triply nonlinear degenerate parabolic problem with zero-flux boundary condition. Accordingly to the case of doubly nonlinear degenerate parabolic hyperbolic equation, we propose a generalization of entropy formulation and prove existence and uniqueness result without any structure condition.展开更多
文摘In this paper,we discuss on the convergence and approximation of an α times integrated semigroups. The Trotter kato theorems for an α times integrated semigroups are obtained.
文摘The α-times integrated C semigroups, α > 0, are introduced and analyzed. The Laplace inverse transformation for α-times integrated C semigroups is obtained, some known results are generalized.
文摘We establish some left and right multiplicative perturbations of a local α-timesintegrated C-semigroup S（·） on a complex Banach space X with non-densely defined genera- tor, which can be applied to obtain some additive perturbation results concerning S（·）. Some growth conditions of the perturbations of S（·） are also established.
文摘The infinite generator of α-times Integrated C semigroups and the properties of resolvent are given. At the same time, we discuss the relationship between the existence of strong solution of a class of nonhomogeneous abstract Cauchy problem and α-times integrated C semigroups, and a sufficient and necessary condition is obtained.
文摘In this paper, based on the theories of α-times Integrated Cosine Function, we discuss the approximation theorem for α-times Integrated Cosine Function and conclude the approximation theorem of exponentially bounded α-times Integrated Cosine Function by the approximation theorem of n-times integrated semigroups. If the semigroups are equicontinuous at each point ? , we give different methods to prove the theorem.
基金This project is supported by the National Science Foundation of China.
文摘In this paper, by Laplace transform version of the Trotter-Kato approximation theorem and the integrated C-semigroup introduced by Myadera, the authors obtained some Trotter-Kato approximation theorems on exponentially bounded C-semigroups, where the range of C (and so the domain of the generator) may not be dense. The authors deduced the corresponding results on exponentially bounded integrated semigroups with nondensely generators. The results of this paper extended and perfected the results given by Lizama, Park and Zheng.
文摘Integrated semigroups which are not exponentially bounded have been studied. The integrated solutions of inhomogeneous and nonlinear abstract Caucby problems are discussed. The reults extends and improves the theorems in [1].
文摘We introduce the notion of the contraction integrated semigroups and give the Lumber-Phillips characterization of the generator, and also the charaterazied generators of isometric integrated semigroups. For their application, a necessary and sufficient condition for q-matrices Q generating a contraction integrated semigroup is given, and a necessary and sufficient condition for a transition function to be a Feller-Reuter-Riley transition function is also given in terms of its q-matrix.
文摘Let T be a singular integral operator bounded on Lp(Rn) for some p, 1 < p < ∞. The authors give a sufficient condition on the kernel of T so that when b ∈BMO, the commutator [b,T](f) = T(bf) - bT(f) is bounded on the space Lp for all p, 1 < p < ∞. The condition of this paper is weaker than the usual pointwise Hormander condition.
基金This project was supported by the National Science Foundation of China
文摘This paper is concerned with applications of integrated semigroups tothe following Cauchy problem:（ACP<sub>n</sub>） x<sup>n</sup>（t）=sum from i=0 to n-1 B<sub>i</sub>x<sup>i</sup>（t）,x<sup>i</sup>（0）=x<sub>i</sub>,0（?）i（?）n-1where B<sub>i</sub> （0（?）i（?）n-1） are closed linear operators on a Banach space X.Auniqueness theorem,a condition of the solvability,a condition of the exponentialwell-posedness,and some results for the special case that B<sub>n-1</sub> is bounded andD(B<sub>n-2</sub>)（?）D（B<sub>i</sub>）（0（?）i（?）n-3） are obtained.
基金Project supported by the National Natural Science Foundation of China and the ABSF of Yunnan Province.
文摘A well-known result established by Arendt in 1987 with regard to the Laplace transforms in Banach spaces is developed. A Widder-Arendt theorem in the setting of sequentially complete locally convex spaces is set up (Theorem 1.1). Moreover, integrated semigroups in such spaces are introduced and generation theorems and some basic properties for semigroups of this type are obtained. As examples, elliptic differential operators on certain classes of function spaces with locally convex topology are shown to be the generators of integrated semigroups under some conditions.
基金The Science and Technology Research(Z2014057)of Higher Education in Hebei Provincethe Doctoral Foundation(L2015B05)of Hebei Normal Universitythe NSF(A2015403040)of Hebei Province
文摘Let L be the infinitesimal generator of an analytic semigroup on L;（R;）with pointwise upper bounds on heat kernel,and denote by L;the fractional integrals of L.For a BMO function b（x）,we show a weak type Llog L estimate of the commutators [b,L;]（f）(x) = b（x）L;（f）(x)-L;（bf）(x).We give applications to large classes of differential operators such as the Schr¨odinger operators and second-order elliptic operators of divergence form.
文摘In this note, we investigated existence and uniqueness of entropy solution for triply nonlinear degenerate parabolic problem with zero-flux boundary condition. Accordingly to the case of doubly nonlinear degenerate parabolic hyperbolic equation, we propose a generalization of entropy formulation and prove existence and uniqueness result without any structure condition.
