Instability of steady states for nonlinear wave and heat equations

We consider time-independent solutions of hyperbolic equations such as \d_{tt}u -\Delta u= f(x,u) where $f$ is convex in $u$. We prove that linear instability with a positive eigenfunction implies nonlinear instability. In some cases the instability occurs as a blow up in finite time. We prove the same result for parabolic equations such as \d_t u -\Delta u= f(x,u). Then we treat several examples under very sharp conditions, including equations with potential terms and equations with supercritical nonlinearities

The Fictions of Surrealism

Surrealism is an attitude toward life, even more than a literary and artistic movement. It aspired to no less than the remaking of man and the world by reintroducing everyday magic and a new idealization of the Female. In many respects, its goal was spiritual renewal. This enterprise was most prominently successful in the domain of poetry and painting. The major spokesman for the movement, Andre Breton, disliked the novel. Nevertheless, the members of the movement and their associates made numerous ventures into prose fiction, with notable results. Four types of fiction are delineated: the neo-Gothic romance; the adventure diary of magic experience—this one being probably the most typical of all the kinds of narrative invented; the erotic (or pornographic) récit, and the linguistic extravaganza, in which language becomes the major instrument of sorcery. In many ways, the Surrealist experiment could be characterized as an attempt at the liberation of languages. This observation raises a number of questions about the impact of Surrealism on subsequent developments in French fiction (and the theatre), as well as upon its impact on Western fiction in general. The conclusion drawn is that Surrealist fiction has been a major contribution, a pioneering effort, in the shaking up of narrative concepts and techniques in the second half of the twentieth century