Assume that Ω is a bounded domain in Rn with n ≥ 2. We study positive solutions to the problem, ∆u = up in Ω, u(x)→∞ as x→ ∂Ω, where p > 1. Such solutions are called boundary blow-up solutions of ∆u = up. We show that a boundary blow-up solution exists in any bounded domain if 1 < p < n n−2 . In particular, when n = 2, there exists a boundary blow-up solution to ∆u = up for all p ∈ (1,∞). We al...

According to Jill Walker, associate professor of humanistic informatics at the University of Bergen, a blog (short for "web log") "is a frequently updated website consisting of dated entries arranged in reverse chronological order so the most recent post appears first (see temporal ordering). Typically, weblogs are published by individuals and their style is personal and informal. Weblogs first...

Free will and human agency are considered foundational for ascriptions of criminal responsibility in Anglo-American jurisprudence. As United States Supreme Court Justice Oliver Wendell Holmes famously observed, "even a dog distinguishes major support from the law firm of Leonard, Street and Deinard, and then presented at a conference on "Neuroethics and Empirical Moral Psychology" at the Depart...

Piston scuffing is one of the destructive faults in internal combustion (IC) engines. There are different causes to make this fault that lack of lubricant is the most important one among them. The purpose of this paper is the quantitative study of the piston scuffing effects on the engine performance parameters which is a new research direction in the IC engine filed. For this reason, several e...

Conventionally, to learn wave collapse and optical turbulence, one must study finite-time blow-up solutions of one-component self-focusing nonlinear Schrödinger equations (NLSE). Here we consider simultaneous blow-up solutions of two-component system of self-focusing NLSE. By studying the associated self-similar solutions, we prove two components of solutions blow up at the same time. These sel...

Based on the thermodynamic theory, the dependence of sublimation energy of metal on temperature and pressure is discussed, and the results indicate that the sublimation energy decreases linearly with the increase of temperature and pressure. Combined with this result, the blow-off impulse of aluminum induced by pulsed X-ray is simulated by smoothed particle hydrodynamics (SPH) method. The numer...

For a sequence of blow up solutions of the Yamabe equation on non-locally conformally flat compact Riemannian manifolds of dimension 10 or 11, we establish sharp estimates on its asymptotic profile near blow up points as well as sharp decay estimates of the Weyl tensor and its covariant derivatives at blow up points. If the Positive Mass Theorem held in dimensions 10 and 11, these estimates wou...

Abstract In this paper, we investigate the blow-up properties of a quasilinear reaction-diffusion system with nonlocal nonlinear sources and weighted nonlocal Dirichlet boundary conditions. The critical exponent is determined under various situations of the weight functions. It is observed that the boundary weight functions play an important role in determining the blow-up conditions. In additi...