Positive radial solutions of the Dirichlet problem for the Minkowski-Curvature equation in a ball

We study the existence and multiplicity of positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation { -div(del upsilon/root 1-vertical bar del upsilon vertical bar(2)) in B-R, upsilon=0 on partial derivative B-R,B- where B-R is a ball in R-N (N >= 2). According to the behaviour off = f (r, s) near s = 0, we prove the existence of either one, two or three positive solutions. All results are obtained by reduction to an equivalent non-singular one-dimensional problem, to which variational methods can be applied in a standard way.

Travelling wave profiles in some models with nonlinear diffusion

We study some properties of the monotone solutions of the boundary value problem (p(u'))' - cu' + f(u) = 0, u(-infinity) = 0, u(+infinity) = 1, where f is a continuous function, positive in (0, 1) and taking the value zero at 0 and 1, and P may be an increasing homeomorphism of (0, 1) or (0, +infinity) onto [0, +infinity). This problem arises when we look for travelling waves for the reaction diffusion equation partial derivative u/partial derivative t = partial derivative/partial derivative x [p(partial derivative u/partial derivative x)] + f(u) with the parameter c representing the wave speed. A possible model for the nonlinear diffusion is the relativistic curvature operator p(nu)= nu/root 1-nu(2). The same ideas apply when P is given by the one- dimensional p- Laplacian P(v) = |v|(p-2)v. In this case, an advection term is also considered. We show that, as for the classical Fisher- Kolmogorov- Petrovski- Piskounov equations, there is an interval of admissible speeds c and we give characterisations of the critical speed c. We also present some examples of exact solutions. (C) 2014 Elsevier Inc. All rights reserved.

A numerical analysis of generalized Boussinesq-type equation using continuos/discontinuous FEM

An improved class of Boussinesq systems of an arbitrary order using a wave surface elevation and velocity potential formulation is derived. Dissipative effects and wave generation due to a time-dependent varying seabed are included. Thus, high-order source functions are considered. For the reduction of the system order and maintenance of some dispersive characteristics of the higher-order models, an extra O(mu 2n+2) term (n ??? N) is included in the velocity potential expansion. We introduce a nonlocal continuous/discontinuous Galerkin FEM with inner penalty terms to calculate the numerical solutions of the improved fourth-order models. The discretization of the spatial variables is made using continuous P2 Lagrange elements. A predictor-corrector scheme with an initialization given by an explicit RungeKutta method is also used for the time-variable integration. Moreover, a CFL-type condition is deduced for the linear problem with a constant bathymetry. To demonstrate the applicability of the model, we considered several test cases. Improved stability is achieved.

Hydrogenating activity of Pt/zeolite catalysts focusing acid support and metal dispersion influence

Toluene hydrogenation was studied over catalysts based on Pt supported on large pore zeolites (HUSY and HBEA) with different metal/acid ratios. Acidity of zeolites was assessed by pyridine adsorption followed by FTIR showing only small changes before and after Pt introduction. Metal dispersion was determined by H2–O2 titration and verified by a linear correlation with the intensity of Pt0–CO band obtained by in situ FTIR. It was also observed that the electronic properties of Pt0 clusters were similar for the different catalysts. Catalytic tests showed rapid catalyst deactivation with an activity loss of 80–95% after 60 min of reaction. The turnover frequency of fresh catalysts depended both on metal dispersion and the support. For the same support, it changed by a 1.7-fold (HBEA) and 4.0-fold (HUSY) showing that toluene hydrogenation is structure-sensitive, i.e. hydrogenating activity is not a unique function of accessible metal. This was proposed to be due to the contribution to the overall activity of the hydrogenation of adsorbed toluene on acid sites via hydrogen spillover. Taking into account the role of zeolite acidity, the catalysts series were compared by the activity per total adsorbing sites which was observed to increase steadily with nPt/(nPt + nA). An increase of the accessible Pt atoms leads to an increase on the amount of spilled over hydrogen available in acid sites therefore increasing the overall activity. Pt/HBEA catalysts were found to be more active per total adsorbing site than Pt/HUSY which is proposed to be due to an augmentation in the efficiency of spilled over hydrogen diffusion related to the proximity between Pt clusters and acid sites. The intervention of Lewis acid sites in a greater extent than that measured by pyridine adsorption may also contribute to this higher activity of Pt/HBEA catalysts. These results reinforce the importance of model reactions as a closer perspective to the relevant catalyst properties in reaction conditions.