EXISTENCE，UNIQUENESS AND PROPERTIES OF THE SOLUTIONS OF A DEGENERATE PARABOLIC EQUATION WITH DIFFUSION－ADVECTION－ABSORPTION

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Existence and uniqueness of positive solutions for higher order nonlocal fractional differential equations

By means of a monotone iterative technique, we establish the existence and uniqueness of the positive solutions for a class of higher conjugate-type fractional differential equation with one nonlocal term. In addition, the iterative sequences of solution and error estimation are also given. In particular, this model comes from economics, financial mathematics and other applied sciences, since the initial value of the iterative sequence can begin from an known function, this is simpler and helpful for computation.     

Existence and uniqueness of steady solutions to the magnetohydrodynamic equations of compressible flows

We establish the existence and uniqueness of a strong solution to the steady magnetohydrodynamic equations for the compressible barotropic fluids in a bounded smooth domain with a perfectly conducting boundary, under the assumption that the external force field is small.     

Existence and uniqueness results for third-order nonlinear differential systems

Sufficient conditions are given for the existence of solutions to third order boundary value problems for nonlinear differential systems. Some appropriate conditions are given to guarantee that the Nagumo condition is satisfied. By constructing appropriate a lower solution-upper solution pair, a concept that is defined in this paper, the uniqueness result of the problem is also established. The emphasis here is that the differential systems has nonlinear dependence on all over order derivatives and the boundary conditions are nonlinear.     

Existence and uniqueness of mild solutions to a semilinear integrodifferential equation of fractional order

In this paper, we prove some existence and uniqueness of mild solutions for a semilinear integrodifferential equation of fractional order with nonlocal initial conditions in α-norm. We assume that the linear part generates a noncompact analytic semigroup. Our results cover the cases that the nonlinearity F takes values in different spaces such as X,X_α and X_β, where α≤β(0,1). Finally, some practical consequences are also obtained.     

Existence and uniqueness of weak solutions for a system applied to image decomposition

In this paper, we prove the existence and uniqueness of weak solutions for a singular evolutionary system, which is deduced from a model for image decomposition combining staircase reduction and texture extraction. The main method we used is p-Laplace regularization. The numerical experimental result shows the efficiency of this kind of model.     

Existence and uniqueness of solutions for a diffusion model of host-parasite dynamics

Milner and Patton (J. Comput. Appl. Math., in press) introduced earlier a new approach to modeling host-parasite dynamics through a convection-diffusion partial differential equation, which uses the parasite density as a continuous structure variable. A motivation for the model was presented there, as well as results from numerical simulations and comparisons with those from other models. However, no proof of existence or uniqueness of solutions to the new model proposed was included there. In the present work the authors deal with the well posedness of that model and they prove existence and uniqueness of solutions, as well as establishing some asymptotic results.     

Existence and uniqueness of weak solutions for a non-uniformly parabolic equation

In this paper we develop a unifying method to prove the existence and uniqueness of weak solutions for the initial-boundary value problem of a non-uniformly parabolic equation. Some well-known parabolic equations are the special cases of this equation.     

Existence and uniqueness of solutions of semilinear stochastic infinite-dimensional differential systems with H-regular noise

Existence and uniqueness of approximate strong solutions of stochastic infinite-dimensional systems

     

Existence and uniqueness of solutions of initial value problems for nonlinear langevin equation involving two fractional orders

The solvability of initial value problems for nonlinear Langevin equation involving two fractional orders are discussed in this paper. An existence result for the solution is obtained using the Leray–Schauder nonlinear alternative. In addition, sufficient conditions for unique solution are established under the Banach contraction principle. The existence results for the initial value problems of nonlinear classical Langevin equation follow as a special case of our results.     

Existence and uniqueness of solutions for the Lane, Emden and Fowler type problem

This paper deals with the existence and uniqueness of a positive solution to the semilinear elliptic equation of the Lane, Emden and Fowler type.     

Existence and uniqueness of solutions for singular integral equation

Using the mixed monotone method we establish existence and uniqueness results for a singular integral equation. The theorem obtained is very general and complements previous known results. The work was supported by the National Natural Science Foundation of China (No.10571021 and No.10701020) and Key Laboratory for Applied Statistics of MOE(KLAS) and Subject Foundation of Harbin University (No. HXK200714).     

Existence and uniqueness of solutions to an electrochemistry system

Existence and partial uniqueness results are established,under a variety of conditions, for a system of equations arising in electrochemistry problems. The main idea is the reduction of the system to a single equation involving nonlocal terms. Upper and lower solution procedures are then applied to show both existence and uniqueness. In this way, results are obtained in more than one space dimension.     

Existence and uniqueness of the solution to the viscoelastic equations for Koiter shells

In this paper, we consider the linearly viscoelastic equations for Koiter shells. The existence and uniqueness of the solution are proved by Galerkin method.     

Existence of global solutions and invariant measures for stochastic differential equations driven by Poisson type noise with non-Lipschitz coefficients

The purpose of this paper is twofold. Firstly, we investigate the problem of existence and uniqueness of solutions to stochastic differential equations with one sided dissipative drift driven by semi-martingales. Secondly, we investigate the problem of existence of an invariant measure for such equations when the coefficients are time independent.     

Existence and uniqueness of periodic solutions for forced Rayleigh-type equations

In this paper, we use the coincidence degree theory to establish new results on the existence and uniqueness of T-periodic solutions for a kind of forced Rayleigh equation of the form

x^″+f(x^′(t))+g(t,x(t))=e(t).     

由Levy过程驱动的倒向随机微分方程在局部Bihari条件下解的存在唯一性

本文利用推广的Bihari不等式和截断函数,证明了由Levy过程驱动的倒向随机微分方程在局部Bihari条件下解的存在唯一性。我们先给出在某种较弱的条件下,方程在局部区间[T0,T],明上解的存在唯一性,然后加强条件,得到解的全局存在唯一性,从而推广了周和秦的结论。     

Existence and uniqueness of local solutions to a class of quasilinear degenerate parabolic systems

In this paper, the authors study an initial and boundary value problem to a system of evolution p-Laplacian equations coupled with general nonlinear terms. The authors use the method of regularization to construct a sequence of approximation solutions with the help of monotone iteration technique and hence obtain the existence of solutions to a regularized system of equations. Then the existence of solutions to the system of evolution p-Laplacian equations is obtained with the use of a standard limiting process. The uniqueness of the solution is also proven.