In the present work, we establish an optimal estimate for the electric potential difference between closely adjacent spherical perfect conductors in n dimensional space (n ≥ 2). This result indicates that electric fields blow up as a pair of spherical perfect conductors approach each other, and provides the lower bound with the optimal blowup rate which was recently established by Bao, Li and Y...

This work deals with a semilinear parabolic systemwhich is coupled both in the equations and in the boundary conditions. The blow-up phenomena of its positive solutions are studied using the scaling method, the Green function and Schauder estimates. The upper and lower bounds of blow-up rates are then obtained. Moreover we show the influences of the reaction terms and the boundary absorption te...

We study numerical approximations to solutions of a system of two nonlinear diffusion equations in a bounded interval, coupled at the boundary in a nonlinear way. In certain cases the system develops a blow-up singularity in finite time. Fixed mesh methods are not well suited to approximate the problem near the singularity. As an alternative to reproduce the behaviour of the continuous solution...

In the present work, we derive that electric fields blow up as a pair of spherical perfect conductors approach each other, and calculate the blow-up rate by a simple method. In the case of two dimensional space, referring to an anti-plane shear model, we can assume that the conductors and the electric fields represent the cross-sections of parallel stiff fibers and the stresses, respectively. H...

In this work, we investigate the following Kirchhoff-type equation with variable exponent nonlinearities u_{tt}-M(‖∇u‖²)△u+|u_{t}|^{p(x)-2}u_{t}=|u|^{q(x)-2}u. We proved the blow up of solutions in finite time by using modified energy functional method.

Referring to the query complexity of testing graph properties in the adjacency matrix model, we advance the study of the class of properties that can be tested non-adaptively within complexity that is inversely proportional to the proximity parameter. Arguably, this is the lowest meaningful complexity class in this model, and we show that it contains a very natural class of graph properties. Sp...