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.     

BIFURCATION SOLUTION BRANCHESAND THEIR NUMERICAL APPROXIMATIONS OF A SEMI-LINEAR ELLIPTIC PROBLEM WITH TWO PARAMETERS

1.IntroductionConsidertheequationdependingontheparametersA,pER,wheref'R-Rands:R-RaresmoothoddfunctionandLetS'u(x)-u(T--x),r={S,I}.Then(l.l)isr-equivalent.Theequality(l.Za)isjustanormalizationoffatx=0.WeintroduceaSobolevspaceX:=Ha(0,7),anddefineamappingT'gEL'(0,T)u'=TaEXimplicitly'Aweakformof(1.1)inXxRZisDuetof(0)~0,theproblem(1.3)(resp.(1))hasatrivialsolutioncurveIfwerestrictp=0,then(l.3)reducestoaproblemwithsingleparameteranditsbifurcationsonthetrivialsolutioncurveCOarewellknown,…     

On the elliptic equation on complete Riemannian manifolds and their geometric applications

We study the elliptic equation on complete noncompact Riemannian manifolds with nonnegative. Three fundamental theorems for this equation are proved in this paper. Complete analyses of this equation on the Euclidean space and the hyperbolic space are carried out when is a constant. Its application to the problem of conformal deformation of nonpositive scalar curvature will be done in the second part of this paper.

     

半线性抛物型方程组解的整体存在性与爆破速率估计

研究了具有非线性热源的半线性抛物型方程组的齐次neumann问题解的爆破性质.利用上下解方法得到了解整体存在的条件与爆破条件,并利用FriedmannMcleod方法建立了爆破速率估计.     

Categories of Projective Geometries with Morphisms and Homomorphisms

Projective geometries studied as Pasch geometries possess morphisms and homomorphisms. A homomorphic image of a projective geometry is shown to be projective. A projective geometry is shown to be Desarguesian iff it is a homomorphic image of a higher dimensional one, which in a sense is dual to the classical imbedding theorem. Semi-linear maps induce morphisms which are homomorphisms iff the associated homomorphisms of skewfields are isomorphisms. Projective geometries form categories with morphisms as well as homomorphisms and Desarguesian ones form a subcategory with Desarguesian homomorphisms.     

Local Estimates of Singular Solution to Gaussian Curvature Equation

In this paper, we derive the local estimates of a singular solution near its singular set Z of the Gaussian curvature equation Δu(x) + K(x)e^{u(x)} = 0 in Ω \ Z, in the case that K(x) may be zero on Z, where Ω ⊂ R² is a bounded open domain, and Z is a set of finite points.     

Multi-mesh Adaptive Finite Element Algorithms for Constrained Optimal Control Problems Governed By Semi-Linear Parabolic Equations

In this paper, we derive a posteriori error estimators for the constrained optimal control problems governed by semi-linear parabolic equations under some assumptions. Then we use them to construct reliable and efficient multi-mesh adaptive finite element algorithms for the optimal control problems. Some numerical experiments are presented to illustrate the theoretical results.