Search results for "Arabo"
showing 10 items of 151 documents
Functional A Posteriori Error Estimates for Time-Periodic Parabolic Optimal Control Problems
2015
This article is devoted to the a posteriori error analysis of multiharmonic finite element approximations to distributed optimal control problems with time-periodic state equations of parabolic type. We derive a posteriori estimates of the functional type, which are easily computable and provide guaranteed upper bounds for the state and co-state errors as well as for the cost functional. These theoretical results are confirmed by several numerical tests that show high efficiency of the a posteriori error bounds. peerReviewed
Boundary regularity for degenerate and singular parabolic equations
2013
We characterise regular boundary points of the parabolic $p$-Laplacian in terms of a family of barriers, both when $p>2$ and $1<p<2$. Due to the fact that $p\not=2$, it turns out that one can multiply the $p$-Laplace operator by a positive constant, without affecting the regularity of a boundary point. By constructing suitable families of barriers, we give some simple geometric conditions that ensure the regularity of boundary points.
Normal forms and embeddings for power-log transseries
2016
First return maps in the neighborhood of hyperbolic polycycles have their asymptotic expansion as Dulac series, which are series with power-logarithm monomials. We extend the class of Dulac series to an algebra of power-logarithm transseries. Inside this new algebra, we provide formal normal forms of power-log transseries and a formal embedding theorem. The questions of classifications and of embeddings of germs into flows of vector fields are common problems in dynamical systems. Aside from that, our motivation for this work comes from fractal analysis of orbits of first return maps around hyperbolic polycycles. This is a joint work with Pavao Mardešić, Jean-Philippe Rolin and Vesna Župano…
Indefinite integrals of special functions from inhomogeneous differential equations
2018
A method is presented for deriving integrals of special functions which obey inhomogeneous second-order linear differential equations. Inhomogeneous equations are readily derived for functions sati...
Control of essential supremum of solutions of quasilinear degenerate parabolic equations
2001
Sufficient conditions are obtained so that a weak subsolution of a class of quasilinear degenerate parabolic equations, bounded from above on theparabolic boundary of the cylinder Q, turns out to be bounded from above in Q.
On the definition of viscosity solutions for parabolic equations
2001
In this short note we suggest a refinement for the definition of viscosity solutions for parabolic equations. The new version of the definition is equivalent to the usual one and it better adapts to the properties of parabolic equations. The basic idea is to determine the admissibility of a test function based on its behavior prior to the given moment of time and ignore what happens at times after that.
Use of Quantitative Morphological Analysis Combined with a Large Sample Size for Estimating Morphological Variability in a Case Study of Armoured Mit…
2015
Abstract The morphology of Oribatida and similar little-known groups of organisms varies considerably, which complicates morphological analysis (e.g. species descriptions). Qualitative analyses have been carried out mostly on a small number of individuals (n < 25). There is lack of studies dealing with mechanisms of how that variation can change in relation to sample size and insufficient discussion on whether qualitative or quantitative analysis is more appropriate for description of morphological variability. A total of 500 adult Carabodes subarcticus Trägårdh, 1902 Oribatida were collected from a local population. Six qualitative and six quantitative traits were characterised using li…
Diffusion Equations with Finite Speed of Propagation
2007
In this paper we summarize some of our recent results on diffusion equations with finite speed of propagation. These equations have been introduced to correct the infinite speed of propagation predicted by the classical linear diffusion theory.
Optimal control for state constrained two-phase Stefan problems
1991
We give a new approach to state constrained control problems associated to non-degenerate nonlinear parabolic equations of Stefan type. We obtain uniform estimates for the violation of the constraints.
QUALITATIVE PROPERTIES OF THE SOLUTIONS OF A NONLINEAR FLUX-LIMITED EQUATION ARISING IN THE TRANSPORT OF MORPHOGENS
2011
In this paper we study some qualitative properties of the solutions of a nonlinear flux-limited equation arising in the transport of morphogens in biological systems. Questions related to the existence of steady states, the finite speed of propagating fronts or the regularization in the interior of the support are studied from analytical and numerical points of view.