Search results for "bound"

Classification and non-existence results for weak solutions to quasilinear elliptic equations with Neumann or Robin boundary conditions

2021

Abstract We classify positive solutions to a class of quasilinear equations with Neumann or Robin boundary conditions in convex domains. Our main tool is an integral formula involving the trace of some relevant quantities for the problem. Under a suitable condition on the nonlinearity, a relevant consequence of our results is that we can extend to weak solutions a celebrated result obtained for stable solutions by Casten and Holland and by Matano.

A delay time bound for distributed parameter circuits with bipolar transistors

1990

We prove here a stability theorem concerning a parabolic system of equations with non-linear boundary conditions that governs the behaviour of a class of networks in which the bipolar transistors operating under large-signal conditions are interconnected with reg-lines modelled by telegraph equations

A Mountain Pass Theorem for a Suitable Class of Functions

2009

Existence of viscosity solutions to two-phase problems for fully nonlinear equations with distributed sources

2018

In this paper we construct a viscosity solution of a two-phase free boundary problem for a class of fully nonlinear equation with distributed sources, via an adaptation of the Perron method. Our results extend those in [Caffarelli, 1988], [Wang, 2003] for the homogeneous case, and of [De Silva, Ferrari, Salsa, 2015] for divergence form operators with right hand side.

Impulsive control of the bilinear Schrödinger equation: propagators and attainable sets

2019

International audience; We consider a linear Schrödinger equation with an unbounded bilinear control term. The control term is the derivative of function with bounded variations (impulsive control). Well-posedness results and regularity of the associated propagators follow from classical theory from Kato. As a byproduct, one obtains a topological obstruction to exact controllability of the system in the spirit of the results of Ball, Marsden and Slemrod.

Semmes surfaces and intrinsic Lipschitz graphs in the Heisenberg group

2018

A Semmes surface in the Heisenberg group is a closed set $S$ that is upper Ahlfors-regular with codimension one and satisfies the following condition, referred to as Condition B. Every ball $B(x,r)$ with $x \in S$ and $0 < r < \operatorname{diam} S$ contains two balls with radii comparable to $r$ which are contained in different connected components of the complement of $S$. Analogous sets in Euclidean spaces were introduced by Semmes in the late $80$'s. We prove that Semmes surfaces in the Heisenberg group are lower Ahlfors-regular with codimension one and have big pieces of intrinsic Lipschitz graphs. In particular, our result applies to the boundary of chord-arc domains and of redu…

A numerical model of the cloud-topped planetary boundary-layer: Impact of aerosol particles on the radiative forcing of stratiform clouds

1997

In a numerical sensitivity study, the microphysical model of stratus MISTRA, is used to investigate the impact of aerosol particles on the evolution of stratiform clouds. Four model runs are presented, each for a different type of background aerosol. Two include aerosol particle size-distributions which are typical of marine and rural continental air masses; a third represents a mixture of marine and rural continental aerosol particles, and the fourth rural continental aerosol particles with a reduced solubility in water. The results show that the microphysical structure of layer clouds was strongly affected by the physico-chemical properties of the aerosol particles from which the cloud dr…

A numerical model of the cloud-topped planetary boundary-layer: radiative forcing of aerosols in stratiform clouds

1998

In a numerical sensitivity study with the microphysical stratus model MISTRA the impact of aerosol particles on the time evolution of stratiform clouds is investigated. Four model runs with different aerosol size distributions are presented. Two size distributions are typical for maritime and continental air masses. The third model run consists of a mixture of maritime and rural aerosol particles, while in the fourth case study rural aerosol particles with a reduced water solubility are utilized. The numerical results show that the microphysical structure of the clouds is strongly affected by the physico-chemical properties of the aerosol particles. In the maritime case, with a relatively l…

The on-line curvilinear component analysis (onCCA) for real-time data reduction

2015

Real time pattern recognition applications often deal with high dimensional data, which require a data reduction step which is only performed offline. However, this loses the possibility of adaption to a changing environment. This is also true for other applications different from pattern recognition, like data visualization for input inspection. Only linear projections, like the principal component analysis, can work in real time by using iterative algorithms while all known nonlinear techniques cannot be implemented in such a way and actually always work on the whole database at each epoch. Among these nonlinear tools, the Curvilinear Component Analysis (CCA), which is a non-convex techni…

Numerical modelling of fatigue crack initiation of martensitic steel

2010

Numerical simulation of micro-crack initiation that is based on Tanaka-Mura micro-crack nucleation model is presented. Three improvements were added to this model. Firstly, multiple slip bands where micro-cracks may occur are used in each grain. Second improvement deals with micro-crack coalescence by extending existing micro-cracks along grain boundaries and connecting them into a macro-crack. The third improvement handles segmented micro-crack generation, where a micro-crack is not nucleated in one step like in Tanaka-Mura model, but is instead generated in multiple steps. Numerical simulation of crack-initiation was performed with ABAQUS, using a plug-in that was written specially for ha…