A lattice Boltzmann type pseudo-kineticmodel for a non-homogeneous Helmholtz equation is derived in this paper. Numerical results for some model problems show the robustness and efficiency of this lattice Boltzmann type pseudo-kinetic scheme. The computation at each site is determined only by local parameters, and can be easily adapted to solve multiple scattering problems with many scatterers or wave propagation in nonhomogeneous medium without increasing the computational cost.

The authors prove the global null controllability for the 1-dimensional nonlinear slow diffusion equation by using both a boundary and an internal control. They assume that the internal control is only time dependent. The proof relies on the return method in combination with some local controllability results for nondegenerate equations and rescaling techniques.

The authors study the Cauchy problem for the semi-linear damped wave equation $u_{tt} - \Delta u + b\left( t \right)u_t = f\left( u \right), u\left( {0,x} \right) = u_0 \left( x \right), u_t \left( {0,x} \right) = u_1 \left( x \right)$ in any space dimension n ≥ 1. It is assumed that the time-dependent damping term b(t) > 0 is effective, and in particular tb(t) → ∞ as t → ∞. The global existence of small energy data solutions for |f(u)| ≈ |u| ^p in the supercritical case of $p > \tfrac{2}{n}$ and $p \leqslant \tfrac{n}{{n - 2}}$ for n ≥ 3 is proved.

Under an appropriate oscillating behavior either at zero or at infinity of the nonlinear data, the existence of a sequence of weak solutions for parametric quasilinear systems of the gradient-type on the Sierpiński gasket is proved. Moreover, by adopting the same hypotheses on the potential and in presence of suitable small perturbations, the same conclusion is achieved. The approach is based on variational methods and on certain analytic and geometrical properties of the Sierpiński fractal as, for instance, a compact embedding result due to Fukushima and Shima.

This paper is devoted to describing the asymptotic behavior of a structure made by a thin plate and a thin perpendicular rod in the framework of nonlinear elasticity. The authors scale the applied forces in such a way that the level of the total elastic energy leads to the Von-Kármán’s equations (or the linear model for smaller forces) in the plate and to a one-dimensional rod-model at the limit. The junction conditions include in particular the continuity of the bending in the plate and the stretching in the rod at the junction.

In the present paper, the solvability condition of the linearized Gauss-Codazzi system and the solutions to the homogenous system are given. In the meantime, the solvability of a relevant linearized Darboux equation is given. The equations are arising in a geometric problem which is concerned with the realization of the Alexandrov’s positive annulus in ℝ³.

The authors prove the Schwarz lemma from a compact complex Finsler manifold to another complex Finsler manifold and any complete complex Finsler manifold with a non-positive holomorphic curvature obeying the Hartogs phenomenon.

In this paper, the Almgren’s frequency function of the following sub-elliptic equation with singular potential on the Heisenberg group: $- \mathcal{L}u + V\left( {z,t} \right)u = - X_i \left( {a_{ij} \left( {z,t} \right)X_j u} \right) + V\left( {z,t} \right)u = 0$ is introduced. The monotonicity property of the frequency is established and a doubling condition is obtained. Consequently, a quantitative proof of the strong unique continuation property for such equation is given.