Periodic Solutions of Third-order Differential Equations with Finite Delay in Vector-valued Functional Spaces

In this paper, we study the well-posedness of the third-order differential equation with finite delay(P_3): αu'"(t) + u"(t) = Au(t) + Bu'(t) + Fut +f(t)(t ∈ T := [0,2π]) with periodic boundary conditions u(0) = u(2π), u'(0) = u"(2π),u"(0)=u"(2π) in periodic Lebesgue-Bochner spaces Lp(T;X) and periodic Besov spaces B_(p,q)~s(T;X), where A and B are closed linear operators on a Banach space X satisfying D(A) ∩ D(B) ≠ {0}, α≠ 0 is a fixed constant and F is a bounded linear operator from Lp([-2π, 0]; X)(resp. Bp,qs([-2π, 0]; X)) into X, ut is given by ut(s) = u(t + s) when s ∈ [-2π,0]. Necessary and sufficient conditions for the Lp-well-posedness(resp. B_(p,q)~s-well-posedness)of(P_3) are given in the above two function spaces. We also give concrete examples that our abstract results may be applied.     

Boundary value problems for a quasilinear parabolic equation with an unknown coefficient

The work is connected with the mathematical modeling of physical–chemical processes in which inner characteristics of materials are subjected to changes. The considered nonlinear parabolic models consist of a boundary value problem for a quasilinear parabolic equation with an unknown coefficient multiplying the derivative with respect to time and, moreover, involve an additional relationship for a time dependence of this coefficient. For such a system, conditions of unique solvability in a class of smooth functions are studied on the basis of the Rothe method. The proposed approach involves the proof of a priori estimates in the difference-continuous Hölder spaces for the corresponding differential-difference nonlinear system that approximates the original system by the Rothe method. These estimates allow one to establish the existence of the smooth solutions and to obtain the error estimates of the approximate solutions.As examples of applications of the considered nonlinear boundary value problems, the models of destruction of heat-protective composite under the influence of high temperature heating are discussed.     

非交换加权Lorentz空间的对偶空间

设μ是一个半有限von Neumann代数.对于0P∞,0q≤∞,定义了非交换加权Lorentz空间Λ_ω~(p,q)(μ)及其associate空间Λ_ω~(p,q)(μ)',给出了空间Λ_ω~(p,q)(μ)'和Λ_ω~(p,q)(μ)'的一些基本性质.应用这些性质,还给出了非交换加权Lorentz空间Λ_ω~p(μ),0P∞的对偶空间.     

Composition operators on Hardy spaces of Riemann surfaces

Our purpose is to define composition operators acting upon Hardy spaces of Riemann surfaces. In terms of counting functions related to analytic self-map on Riemann surfaces, the boundedness and compactness are characterized.     

On the existence,uniqueness and stability of solutions for semi-linear generalized elasticity equation with general damping term

In this paper, we consider a semi-linear generalized hyperbolic boundary value problem associated to the linear elastic equations with general damping term and nonlinearities of variable exponent type. Under suitable conditions, local and global existence theorems are proved. The uniqueness of the solution have been gotten by eliminating some hypotheses that have been imposed by other authors for different particular problems. We show that any solution with nontrivial initial datum becomes stable.     

Existence and Uniqueness of Solution for a Class of Nonlinear Degenerate Elliptic Equations

In this work we are interested in the existence and uniqueness of solutions for the Navier problem associated to the degenerate nonlinear elliptic equations■,in the setting of the weighted Sobolev spaces.     

Parallel and totally geodesic hypersurfaces of non-reductive homogeneous four-manifolds

We classify totally geodesic and parallel hypersurfaces of four-dimensional non-reductive homogeneous pseudo-Riemannian manifolds.