Balls and Quasi-Metrics: A Space of Homogenous Type Modeling the Real Analysis Related to the Monge-Ampère Equation.
We are concerned with the boundedness and large time behaviour of the solution for a system of reaction-diffusion equations modelling complex consecutive reactions on a bounded domain under homogeneous Neumann boundary conditions. Using the techniques of E. Conway, D. Hoff and J. Smoller [3] we also show that the bounded solution converges to a constant function as t → ∞. Finally, we investigate the rate of this convergence.
We prove bilinear virial identities for the nonlinear Schrödinger equation, which are extensions of the Morawetz interaction inequalities. We recover and extend known bilinear improvements to Strichartz inequalities and provide applications to various nonlinear problems, most notably on domains with boundaries.
We study the behaviour of weak solutions (as well as their gradients) of boundary value problems for quasi-linear elliptic divergence equations in domains extending to infinity along a cone.