In this paper, we obtain some global existence results for the higher-dimensionai nonhomogeneous, linear, semilinear and nonlinear thermoviscoelastic systems by using semigroup approach.
Let S be an antinegative commutative semiring having no zero divisions or finite general Boolean Algebra and μ(S) the set of n×n matrices over S. In this paper we characterize the structure of the senigroup n,...Let S be an antinegative commutative semiring having no zero divisions or finite general Boolean Algebra and μ(S) the set of n×n matrices over S. In this paper we characterize the structure of the senigroup n,(S) of linear operators on μn,(S) that strongly preserve the M-P inverses of matrices.展开更多
By using the strong continuous semigroup theory of linear operators we prove the existence of a unique positive time-dependent solution of the model describing a re-pairable, standby, human & machine system.
Consider any traveling wave solution of the Kuramoto-Sivashinsky equation that is asymp-totic to a constant as x→+∞ . The authors prove that it is nonlinearly unstable under Hl perturbations. The proof is based on a...Consider any traveling wave solution of the Kuramoto-Sivashinsky equation that is asymp-totic to a constant as x→+∞ . The authors prove that it is nonlinearly unstable under Hl perturbations. The proof is based on a general theorem in Banach spaces asserting that linear instability implies nonlinear instability.展开更多
In this paper, we propose a non-autonomous convection-reaction diffusion system （CDI） with a nonlinear reaction source function. This model refers to the quantification and the distribution of antibiotic resistant b...In this paper, we propose a non-autonomous convection-reaction diffusion system （CDI） with a nonlinear reaction source function. This model refers to the quantification and the distribution of antibiotic resistant bacteria （ARB） in a river. The main contributions of this paper are： （i） the determination of the limit set of the system by applying the semigroups theory, it is shown that it is reduced to the solutions of the associated elliptic system （CDI）e, （ii） sufficient conditions for the existence of a positive solution of （CDI）e based on the Leray-Schauder＇s degree theory. Numerical simulations which support our theoretical analysis are also given.展开更多
Let V be a linear space over a field F with finite dimension,L(V) the semigroup,under composition,of all linear transformations from V into itself.Suppose that V = V1⊕V2⊕···⊕Vm is a direct sum decomp...Let V be a linear space over a field F with finite dimension,L(V) the semigroup,under composition,of all linear transformations from V into itself.Suppose that V = V1⊕V2⊕···⊕Vm is a direct sum decomposition of V,where V1,V2,...,Vm are subspaces of V with the same dimension.A linear transformation f ∈ L(V) is said to be sum-preserving,if for each i(1 ≤ i ≤ m),there exists some j(1 ≤ j ≤ m) such that f(Vi) ■Vj.It is easy to verify that all sum-preserving linear transformations form a subsemigroup of L(V) which is denoted by L⊕(V).In this paper,we first describe Green's relations on the semigroup L⊕(V).Then we consider the regularity of elements and give a condition for an element in L⊕(V) to be regular.Finally,Green's equivalences for regular elements are also characterized.展开更多
A nonlinear mathematical HIV TB model with infection-age is proposed in this paper. The basic reproduction numbers according to HIV and TB are respectively determined whether one of the diseases dies out or persists. ...A nonlinear mathematical HIV TB model with infection-age is proposed in this paper. The basic reproduction numbers according to HIV and TB are respectively determined whether one of the diseases dies out or persists. The local and global stability of the disease-free and dominated equilibria are discussed by employing integral semigroup theory and Lyapunov functionals. The persistence of the system is also obtained by the persistence theories of the systems. The simulation illustrates the theoretical results.展开更多
基金Supported by the NNSF of China(10571024, 10871040)
文摘In this paper, we obtain some global existence results for the higher-dimensionai nonhomogeneous, linear, semilinear and nonlinear thermoviscoelastic systems by using semigroup approach.
文摘Let S be an antinegative commutative semiring having no zero divisions or finite general Boolean Algebra and μ(S) the set of n×n matrices over S. In this paper we characterize the structure of the senigroup n,(S) of linear operators on μn,(S) that strongly preserve the M-P inverses of matrices.
基金This research is supported by the Tianyuan Mathematics Foundation (No. 10226007) and the Science Foundation of Xinjiang University
文摘By using the strong continuous semigroup theory of linear operators we prove the existence of a unique positive time-dependent solution of the model describing a re-pairable, standby, human & machine system.
基金Project Supported in part by NSFGrant DMS-0071838.
文摘Consider any traveling wave solution of the Kuramoto-Sivashinsky equation that is asymp-totic to a constant as x→+∞ . The authors prove that it is nonlinearly unstable under Hl perturbations. The proof is based on a general theorem in Banach spaces asserting that linear instability implies nonlinear instability.
文摘In this paper, we propose a non-autonomous convection-reaction diffusion system （CDI） with a nonlinear reaction source function. This model refers to the quantification and the distribution of antibiotic resistant bacteria （ARB） in a river. The main contributions of this paper are： （i） the determination of the limit set of the system by applying the semigroups theory, it is shown that it is reduced to the solutions of the associated elliptic system （CDI）e, （ii） sufficient conditions for the existence of a positive solution of （CDI）e based on the Leray-Schauder＇s degree theory. Numerical simulations which support our theoretical analysis are also given.
文摘Let V be a linear space over a field F with finite dimension,L(V) the semigroup,under composition,of all linear transformations from V into itself.Suppose that V = V1⊕V2⊕···⊕Vm is a direct sum decomposition of V,where V1,V2,...,Vm are subspaces of V with the same dimension.A linear transformation f ∈ L(V) is said to be sum-preserving,if for each i(1 ≤ i ≤ m),there exists some j(1 ≤ j ≤ m) such that f(Vi) ■Vj.It is easy to verify that all sum-preserving linear transformations form a subsemigroup of L(V) which is denoted by L⊕(V).In this paper,we first describe Green's relations on the semigroup L⊕(V).Then we consider the regularity of elements and give a condition for an element in L⊕(V) to be regular.Finally,Green's equivalences for regular elements are also characterized.
文摘A nonlinear mathematical HIV TB model with infection-age is proposed in this paper. The basic reproduction numbers according to HIV and TB are respectively determined whether one of the diseases dies out or persists. The local and global stability of the disease-free and dominated equilibria are discussed by employing integral semigroup theory and Lyapunov functionals. The persistence of the system is also obtained by the persistence theories of the systems. The simulation illustrates the theoretical results.
