SUFFICIENT CONDITIONS ON DIFFUSIVITY FOR THE EXISTENCE AND NONEXISTENCE OF STABLE EQUILIBRIA WITH NONLINEAR FLUX ON THE BOUNDARY

A reaction-diffusion equation with variable diffusivity and non-linear flux boundary condition is considered. The goal is to give sufficient conditions on the diffusivity function for nonexistence and also for existence of nonconstant stable stationary solutions. Applications are given for the main result of nonexistence.

Impacts of interruption of the Agulhas leakage on the tropical Atlantic in coupled ocean-atmosphere simulations

In this paper we use a coupled ocean-atmosphere model to investigate the impact of the interruption of Agulhas leakage of Indian ocean water on the tropical Atlantic, a region where strong coupled ocean-atmosphere interactions occur. The effect of a shut down of leakage of Indian ocean water is isolated from the effect of a collapse of the MOC. In our experiments, the ocean model is forced with boundary conditions in the southeastern corner of the domain that correspond to no interocean exchange of Indian ocean water into the Atlantic. The southern boundary condition is taken from the Levitus data and ensures an MOC in the Atlantic. Within this configuration, instead of warm and salty Indian ocean water temperature (cold) and salinity (fresh) anomalies of southern ocean origin propagate into the South Atlantic and eventually reach the equatorial region, mainly in the thermocline. This set up mimics the closure of the ""warm water path"" in favor of the ""cold water path"". As part of the atmospheric response, there is a northward shift of the intertropical convergence zone (ITCZ). The changes in trade winds lead to reduced Ekman pumping in the equatorial region. This leads to a freshening and warming of the surface waters along the equator. Especially in the Cold Tongue region, the cold and fresh subsurface anomalies do not reach the surface due to the reduced upwelling. The anomaly signals are transported by the equatorial undercurrent and spread away from the equator within the thermocline. Part of the anomaly eventually reaches the Tropical North Atlantic, where it affects the Guinea Dome. Surprisingly, the main effect at the surface is small on the equator and relatively large at the Guinea Dome. In the atmosphere, the northward shift of the ITCZ is associated with a band of negative precipitation anomalies and higher salinities over the Tropical South Atlantic. An important implication of these results is that the modified water characteristics due to a shut down of the Agulhas leakage remain largely unaffected when crossing the equatorial Atlantic and therefore can affect the deepwater formation in the North Atlantic. This supports the hypothesis that the Agulhas leakage is an important source region for climate change and decadal variability of the Atlantic.

GROUND STATE AND NON-GROUND STATE SOLUTIONS OF SOME STRONGLY COUPLED ELLIPTIC SYSTEMS

We study an elliptic system of the form Lu = vertical bar v vertical bar(p-1) v and Lv = vertical bar u vertical bar(q-1) u in Omega with homogeneous Dirichlet boundary condition, where Lu := -Delta u in the case of a bounded domain and Lu := -Delta u + u in the cases of an exterior domain or the whole space R-N. We analyze the existence, uniqueness, sign and radial symmetry of ground state solutions and also look for sign changing solutions of the system. More general non-linearities are also considered.

Exponential stability for a plate equation with p-Laplacian and memory terms

This paper is concerned with the energy decay for a class of plate equations with memory and lower order perturbation of p-Laplacian type, utt+?2u-?pu+?0tg(t-s)?u(s)ds-?ut+f(u)=0inOXR+, with simply supported boundary condition, where O is a bounded domain of RN, g?>?0 is a memory kernel that decays exponentially and f(u) is a nonlinear perturbation. This kind of problem without the memory term models elastoplastic flows.

Error Upper Bounds for a Computational Method for Nonlinear Boundary and Initial-Value Problems

This work develops a computational approach for boundary and initial-value problems by using operational matrices, in order to run an evolutive process in a Hilbert space. Besides, upper bounds for errors in the solutions and in their derivatives can be estimated providing accuracy measures.

A nonlinear elliptic problem with terms concentrating in the boundary

In this paper, we investigate the behavior of a family of steady-state solutions of a nonlinear reaction diffusion equation when some reaction and potential terms are concentrated in a e-neighborhood of a portion G of the boundary. We assume that this e-neighborhood shrinks to G as the small parameter e goes to zero. Also, we suppose the upper boundary of this e-strip presents a highly oscillatory behavior. Our main goal here was to show that this family of solutions converges to the solutions of a limit problem, a nonlinear elliptic equation that captures the oscillatory behavior. Indeed, the reaction term and concentrating potential are transformed into a flux condition and a potential on G, which depends on the oscillating neighborhood. Copyright (C) 2012 John Wiley & Sons, Ltd.