Time estimates for the Cauchy problem for a third-order hyperbolic equation.
In this paper, we consider the problem of the existence of conformal metrics with prescribed scalar curvature on the standard sphere S n, n ≥ 3. We give new existence and multiplicity results based on a new Euler-Hopf formula type. Our argument also has the advantage of extending well known results due to Y. Li [16].
We show a locally uniform bound for global nonnegative solutions of the system , in , on , where , and is a bounded domain in , . In particular, the trajectories starting on the boundary of the domain of attraction of the zero solution are global and bounded.
Bounded traveling waves, arising in combustion model for gas-solid reactions in a porous medium, are studied. We consider the existence, uniqueness and several qualitative properties. In particular we investigate waves with finiteness and derive estimates in the limit of vanishing diffusion.