共查询到20条相似文献,搜索用时 31 毫秒
1.
James H. Liu 《Semigroup Forum》2002,66(1):63-67
We provide a counterexample to some recent publications concerning the existence of the mild solutions of the non-local evolution equations, and indicate that in the study of the non-local evolution equations, the operators from which the mild solutions may be derived are in general not compact, thus those fixed point theorems requiring the compactness of the operators are not applicable. 相似文献
2.
James H. Liu 《Semigroup Forum》2008,66(1):63-67
We provide a counterexample to some recent publications concerning the existence of the mild solutions of the non-local evolution
equations, and indicate that in the study of the non-local evolution equations, the operators from which the mild solutions
may be derived are in general not compact, thus those fixed point theorems requiring the compactness of the operators are
not applicable. 相似文献
3.
Several formulations of a local geometric measure-type condition are imposed on super-level sets of mild solutions to the homogeneous incompressible 3D magnetohydrodynamical system with bounded initial data to prevent finite-time singularity formation. Supporting this, results regarding the existence, uniqueness, and real analyticity of mild solutions are established as is a sharp lower bound on the radius of analyticity. 相似文献
4.
In this paper, we investigate the continuous dependence with respect to the initial data of the solutions for the 1D and 1.5D relativistic Vlasov–Maxwell system. More precisely, we prove that these solutions propagate with finite speed. We formulate our results in the framework of mild solutions, i.e., the particle densities are solutions by characteristics and the electro-magnetic fields are Lipschitz continuous functions. 相似文献
5.
《Nonlinear Analysis: Theory, Methods & Applications》2009,70(12):4365-4379
In this paper, we investigate the continuous dependence with respect to the initial data of the solutions for the 1D and 1.5D relativistic Vlasov–Maxwell system. More precisely, we prove that these solutions propagate with finite speed. We formulate our results in the framework of mild solutions, i.e., the particle densities are solutions by characteristics and the electro-magnetic fields are Lipschitz continuous functions. 相似文献
6.
L. Olszowy S. W?drychowicz 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(17):6758-6769
In this paper, we study the existence of mild solutions of a semilinear evolution equation on an unbounded interval. The rapidity of the growth of those solutions is characterized. Moreover, we investigate the local and global attractivity of solutions of an equation in question and we describe their asymptotic behaviour. Our investigations are conducted in a real separable Banach space. 相似文献
7.
In this paper, we are concerned with the initial value problem of a class of damped elastic systems in an order Banach spaces $E$. By employing the method of lower and upper solutions, we discuss the existence of extremal mild solutions between lower and upper mild solutions for such problem with the associated semigroup is equicontinuous. In addition, two examples are given to illustrate our results. 相似文献
8.
In this paper, we study the solvability and optimal controls of a class of fractional integrodifferential evolution systems
with infinite delay in Banach spaces. Firstly, a more appropriate concept for mild solutions is introduced. Secondly, existence
and continuous dependence of mild solutions are investigated by utilizing the techniques of a priori estimation and extension
of step by steps. Finally, existence of optimal controls for system governed by fractional integrodifferential evolution systems
with infinite delay is proved. 相似文献
9.
《Nonlinear Analysis: Hybrid Systems》2008,2(1):28-37
The strong solutions approximation approach for mild solutions of stochastic functional differential equations with Markovian switching driven by Lévy martingales in Hilbert spaces is considered. Asymptotic behaviors with a general decay rate for the second moments of mild solutions of the above equations are obtained. An example is given to illustrate our theory. 相似文献
10.
A novel approach to the global attracting sets of mild solutions for stochastic functional partial differential equations driven by Lévy noise is presented. Consequently, some new sufficient conditions ensuring the existence of the global attracting sets of mild solutions for the considered equations are established. As applications, some new criteria for the exponential stability in mean square of the considered equations is obtained. Subsequently, by employing a weak convergence approach, we try to establish some stability conditions in distribution of the segment processes of mild solutions to stochastic delay partial differential equations with jumps under some weak conditions. Some known results are improved. Lastly, some examples are investigated to illustrate the theory. 相似文献
11.
Some results on the existence and uniqueness of mild solution for a system of semilinear impulsive differential equations with infinite fractional Brownian motions are proved. The approach is based on Perov's fixed point theorem and a new version of Schaefer's fixed point theorem in generalized Banach spaces. The relationship between mild and weak solutions and the exponential stability of mild solutions are investigated as well. The abstract theory is illustrated with an example. 相似文献
12.
In this work we establish existence of mild solutions for a class of abstract semi-linear functional differential equations of second order and we prove that the set consisting of the mild solutions for these problems is connected. 相似文献
13.
In this paper we show the asymptotic stability of the solutions of some differential equations with delay and subject to impulses. After proving the existence of mild solutions on the half-line, we give a Gronwall–Bellman-type theorem. These results are prodromes of the theorem on the asymptotic stability of the mild solutions to a semilinear differential equation with functional delay and impulses in Banach spaces and of its application to a parametric differential equation driving a population dynamics model. 相似文献
14.
This work is devoted to the solvability and finite time blow-up of solutions of the Cauchy problem for the dissipative Boussinesq equation in all space dimension. We prove the existence and uniqueness of local mild solutions in the phase space by means of the contraction mapping principle. By establishing the time-space estimates of the corresponding Green operators, we obtain the continuation principle. Under some restriction on the initial data, we further study the results on existence and uniqueness of global solutions and finite time blow-up of solutions with the initial energy at three different level. Moreover, the sufficient and necessary conditions of finite time blow-up of solutions are given. 相似文献
15.
非局部条件下半线性微分方程的适度解 总被引:1,自引:0,他引:1
讨论了Banach空间中非局部条件下半线性微分方程的适度解的存在性,利用不动点和非紧测度的方法,给出了在不需要半群紧性条件下方程适度解的存在性,并且对f是连续紧算子和f是Lipschitz连续的情形做了统一处理,从而得到了更为广泛和一般性的结果. 相似文献
16.
Abstract In this work, we shall investigate solution (strong, weak and mild) processes and relevant properties of stochastic convolutions for a class of stochastic retarded differential equations in Hilbert spaces. We introduce a strongly continuous one-parameter family of bounded linear operators which will completely describe the corresponding deterministic systematical dynamics with time delays. This family, which constitutes the fundamental solutions (Green's operators) of our stochastic retarded systems, is applied subsequently to define mild solutions of the stochastic retarded differential equations considered. The relations among strong, weak and mild solutions are explored. By virtue of a strong solution approximation method, Burkholder–Davis–Gundy's type of inequalities for stochastic convolutions are established. 相似文献
17.
This article is concerned with a semilinear McKean–Vlasov type stochastic evolution equation in a real Hilbert space. The main goal of the article is to study the existence and uniqueness of mild solutions, Yosida approximations of mild solutions of such equations, and to deduce the weak convergence of the corresponding induced probability measures. As an application, we also study the exponential stability of mild solutions of such equations. 相似文献
18.
Rajesh Dhayal Muslim Malik Syed Abbas Amar Debbouche 《Mathematical Methods in the Applied Sciences》2020,43(7):4107-4124
We study optimal control problems for a class of second-order stochastic differential equation driven by mixed-fractional Brownian motion with non-instantaneous impulses. By using stochastic analysis theory, strongly continuous cosine family, and a fixed point approach, we establish the existence of mild solutions for the stochastic system. Moreover, the optimal control results are derived without uniqueness of mild solutions of the stochastic system. Finally, the main results are validated with the aid of an example. 相似文献
19.
H. R. Henriquez 《Acta Mathematica Hungarica》2008,121(3):203-227
We establish the existence of mild solutions and periodic mild solutions for a class of abstract first-order non-autonomous
neutral functional differential equations with infinite delay in a Banach space.
This research was supported by FONDECYT-CONICYT, Grant 1050314. 相似文献
20.
Kai Liu 《Journal of Theoretical Probability》2012,25(2):565-593
In this work, some regularity properties of mild solutions for a class of stochastic linear functional differential equations
driven by infinite-dimensional Wiener processes are considered. In terms of retarded fundamental solutions, we introduce a
class of stochastic convolutions which naturally arise in the solutions and investigate their Yosida approximants. By means
of the retarded fundamental solutions, we find conditions under which each mild solution permits a continuous modification.
With the aid of Yosida approximation, we study two kinds of regularity properties, temporal and spatial ones, for the retarded
solution processes. By employing a factorization method, we establish a retarded version of the Burkholder–Davis–Gundy inequality
for stochastic convolutions. 相似文献