Boundary Behavior of Large Solutions to the Monge–Ampère Equation in a Borderline Case

This paper is concerned with the boundary behavior of strictly convex large solutions to the Monge–Ampère equation det D^2u(x) = b(x)f(u(x)), u >0, x∈Ω, where Ω is a strictly convex and bounded smooth domain in R^N with N ≥ 2, f is normalized regularly varying at infinity with the critical index N and has a lower term, and b∈C~∞(Ω) is positive in Ω, but may be appropriate singular on the boundary.

Exact boundary behavior of large solutions to semilinear elliptic equations with a nonlinear gradient term

This paper is concerned with exact boundary behavior of large solutions to semilinear elliptic equations △u=b(x)f(u)(C0+|▽u|q),x∈Ω,where Ω is a bounded domain with a smooth boundary in RN,C0≥0,q E [0,2),b∈Clocα(Ω) is positive in but may be vanishing or appropriately singular on the boundary,f∈C[0,∞),f(0)=0,and f is strictly increasing on [0,∞)(or f∈C(R),f(s)> 0,■s∈R,f is strictly increasing on R).We show unified boundary behavior of such solutions to the problem under a new structure condition on f.

A Unified Boundary Behavior of Large Solutions to Hessian Equations

This paper is concerned with strictly k-convex large solutions to Hessian equations Sk(D2u(x))=b(x)f(u(x)),x∈Ω,whereΩis a strictly(k-1)-convex and bounded smooth domain in Rn,b∈C∞(Ω)is positive inΩ,but may be vanishing on the boundary.Under a new structure condition on f at infinity,the author studies the refined boundary behavior of such solutions.The results are obtained in a more general setting than those in[Huang,Y.,Boundary asymptotical behavior of large solutions to Hessian equations,Pacific J.Math.,244,2010,85–98],where f is regularly varying at infinity with index p>k.

ASYMPTOTIC BEHAVIOR FOR A CLASS OF ELLIPTICEQUIVALUED SURFACE BOUNDARY VALUE PROBLEM WITH DISCONTINUOUS INTERFACE CONDITIONS

Spontaneous potential well-logging is one of the important techniques in petroleum exploitation. A spontaneous potential satisfies an elliptic equivalued surface boundary value problem with discontinuous interface conditions. In practice, the measuring electrode is so small that we can simplify the corresponding equivalued surface to a point. In this paper, we give a positive answer to this approximation process:when the equivalued surface shrinks to a point, the solution of the original equivalued surface boundary value problem converges to the solution of the corresponding limit boundary value problem.

BOUNDARY AND ANGULAR LAYER BEHAVIOR IN SINGULARLY PERTURBED SEMILINEAR SYSTEMS

Some authors employed the method and technique of differential inequalities to obtain fairly general results concerning the existence and asymptotic behavior, as ?-n+ , of the solutions of scalar boundary value problemsIn this paper, we extend these results to vector boundary value problems, under analogous stability conditions on the solution u = u(t) of the reduced equation 0 = h(t, u) Two types of asymptotic behavior are studied, depending on whether the reduced solution u(f) has or does not have a con tinuous first derivative in (a, b) leading to the phenomena of boundary and angular layers.

Control of rock joint parameters on deformation of tunnel opening

In this paper, stress behavior of shallow tunnels under simultaneous non-uniform surface traction and symmetric gravity loading was studied using a direct boundary element method（BEM）. The existing fullplane elastostatic fundamental solutions to displacement and stress fields were used and implemented in a developed algorithm. The cross-section of the tunnel was considered in circular, square, and horseshoe shapes and the lateral coefficient of the domain was assumed as unit quantity. Double-node procedure of the BEM was applied at the corners to improve the model including sudden traction changes. The results showed that the method used was a powerful tool for modeling underground openings under various external as well as internal loads. Eccentric loads significantly influenced the stress pattern of the surrounding tunnel. The achievements can be practically used in completing and modifying regulations for stability investigation of shallow tunnels.

Effect of grain boundary on the mechanical behaviors of irradiated metals: a review

The design of high irradiation-resistant materials is very important for the development of next-generation nuclear reactors. Grain boundaries acting as effective defect sinks are thought to be able to moderate the deterioration of mechanical behaviors of irradiated materials, and have drawn increasing attention in recent years. The study of the effect of grain boundaries on the mechanical behaviors of irradiated materials is a multi-scale problem. At the atomic level, grain boundaries can effectively affect the production and formation of irradiation-induced point defects in grain interiors, which leads to the change of density, size distribution and evolution of defect clusters at grain level. The change of microstructure would influence the macroscopic mechanical properties of the irradiated polycrystal. Here we give a brief review about the effect of grain boundaries on the mechanical behaviors of irradiated metals from three scales: microscopic scale, mesoscopic scale and macroscopic scale.

Bainite Growth Behavior at Early Stage of Transformation in a High Carbon Silicon-Containing Steel

The growth behavior at the early stage of bainitic transformation was investigated using optical microscopy,X-ray diffraction analysis and transmission electronic microscopy.The bainite was obtained by isothermal transformation at 200 ℃ only for a short time in a high carbon silicon-containing steel after austenitization at 200 ℃ only for 20 min.Transmission electronic microscopy shows that the bainite appears in the form of plates with a width of about 30 nm,and that the interface of the bainite leading tip is wedge shaped.X-ray diffraction analysis reveals that the bainite plates consist of single ferrite phase,with absence of carbides.The results confirm the occurrence of the moiré which suggests the existence of austenite grain boundaries at the bainite leading tip.Both the lateral growth and longitudinal growth of bainite have weak ability to traverse the lattice-distortion strain fields and austenite grain boundary.The austenite grain boundary impedes the longitudinal growth of the bainite plate,i.e.,the growth of bainite plate stops at the austenite grain boundary.The longitudinal growth of bainite associated with the features of shear mechanism can not completely be in accordance with that of martensitic transformation.

Mechanism of Stress Relief Cracking in a Granular Bainitic Steel

Coarse-grained heat-affected zone（CGHAZ） of a low alloyed,granular bainitic steel T24 was simulated in a Gleeble apparatus.The stress relief of the CGHAZ was analyzed by annealing the samples.The morphology and behavior of the microstructure near the grain boundaries during stress relief were investigated by means of focused ion beam,in situ tensile testing,transmission electron microscopy,scanning electron microscopy and electron back-scatter diffraction.It was observed that there were large martensite/austenite islands distributed along the grain boundaries of CGHAZ.During stress relief at elevated temperature,the retained austenite at the grain boundaries decomposed into M3C carbides and a ferrite forming softening zone.Together with the stress relief,piled up of dislocations occurred within the ferrite in the area adjacent to the ferrite/M3C interface,which resulted in high level of stress accumulation and caused crack initiation along the grain boundaries.These results indicate that the stress relief induced the grain boundary crack is controlled by other mechanisms rather than the creep-like grain boundary sliding.