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1.
We study the Cauchy problem for a nonlinear evolution system with singularintegral differential terms, By means of some a priori estimates of the solution and the Leray-Schander‘s fixed point theorem, we prove the existence and the uniqueness theorems of the generalized global solution of the mentioned problem.  相似文献   

2.
This article deals with a new fractional nonlinear delay evolution system driven by a hemi-variational inequality in a Banach space.Utilizing the KKM theorem,a result concerned with the upper semicontinuity and measurability of the solution set of a hemivariational inequality is established.By using a fixed point theorem for a condensing setvalued map,the nonemptiness and compactness of the set of mild solutions are also obtained for such a system under mild conditions.Finally,an example is presented to illustrate our main results.  相似文献   

3.
Using the boundary layer corrective method,a class of nonlinear disturbed delayed system is studied.The asymptotic solution to the model is constructed.And the asymptotic behaviors of the solution are also discussed.  相似文献   

4.
Under some conditios to find the interaction, of waves is, in the final analysis, to solve kind of anti-symmetric system of second order evolution equations. Thus, in §2 of this paper we discuss the Cauchy problem of anti-symmetric system of second order evolution equations under general situation. It is found that if there is a solution of the system of linear equations corresponding to the anti-symmetric system of second order evolution equations, then for the Cauchy problem there exists a uniqe solution In §3, the abstract boundary value problem of anti-symmetric system of second order evolution equations is studied In §4 we give an example to illuminate the Solvability of initial-boundary value problem about anti-symmetric system of second order evolution equations In the physcial sense, this example is none other then the interaction problem of waves  相似文献   

5.
Based on the work of paper,we propose a modified Levenberg-Marquardt algoithm for solving singular system of nonlinear equations F(x)=0,where F(x):R^n→R^n is continuously differentiable and F‘(x)is Lipschitz continuous.The algorithm is equivalent to a trust region algorithm in some sense,and the global convergence result is given.The sequence generated by the algorithm converges to the solution quadratically,if ||F(x)||2 provides a local error bound for the system of nonlinear equations.Numerical results show that the algorithm performs well.  相似文献   

6.
Soliton solutions of a class of generalized nonlinear evolution equations are discussed ana-lytically and numerically. This is done by using a travelling wave method to formulate one-soliton solution and the finite difference method to the numerical solutions and the interactions betweenthe solitons for the generalized nonlinear Sehrodinger equations. the characteristic behavior of thenonlinearity admintted in the system has been investigated and the soliton states of the system in thelimit when a→Oand a→∞ have been studled. The results presented show that the soliton phe-rtomenon is charaeteristics associated with the nonlinearities of the dynamical systems.  相似文献   

7.
A FREE-BOUNDARY PROBLEM TO DYNAMIC SYSTEM FOR PURE FOREST   总被引:1,自引:0,他引:1  
A free-boundary model of nonlinear dynamic system for pure forest is presented, in which the felling rate is unbounded nearby the free boundary. The effiect of unbounded function on a priori estimate and analysis of regularity is overcome, and the existence and uniqueness of the global classical solution to this system are proved.  相似文献   

8.
In this paper, the authors discuss the global existence and blow-up of the solution to an evolution p-Laplace system with nonlinear sources and nonlinear boundary condition. The authors first establish the local existence of solutions, then give a necessary and sufficient condition on the global existence of the positive solution.  相似文献   

9.
If we knew the existence of upper and lower solutions u, v of a coupled reaction-diffusion system with quasi-monotone nonlinear reaction functions, then we can prove the existence of a solution ω of the same system such that u<ω相似文献   

10.
This paper explores the diffeomorphism of a backward stochastic ordinary differential equation (BSDE) to a system of semi-linear backward stochastic partial differential equations (BSPDEs), under the inverse of a stochastic flow generated by an ordinary stochastic differential equation (SDE). The author develops a new approach to BSPDEs and also provides some new results. The adapted solution of BSPDEs in terms of those of SDEs and BSDEs is constructed. This brings a new insight on BSPDEs, and leads to a probabilistic approach. As a consequence, the existence, uniqueness, and regularity results are obtained for the (classical, Sobolev, and distributional) solution of BSPDEs. The dimension of the space variable x is allowed to be arbitrary n, and BSPDEs are allowed to be nonlinear in both unknown variables, which implies that the BSPDEs may be nonlinear in the gradient. Due to the limitation of space, however, this paper concerns only classical solution of BSPDEs under some more restricted assumptions.  相似文献   

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