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Frequency functions on the Heisenberg group, the uncertainty principle and unique continuation

Nicola Garofalo, Ermanno Lanconelli (1990)

Annales de l'institut Fourier

A recent result of Bahouri shows that continuation from an open set fails in general for solutions of ℒ u = V u where V ∈ C ∞ and ℒ = ∑ j = 1 N - 1 X j 2 is a (nonelliptic) operator in R N satisfying Hörmander’s condition for hypoellipticity. In this paper we study the model case when ℒ is the subelliptic Laplacian on the Heisenberg group and V is a zero order term which is allowed to be unbounded. We provide a sufficient condition, involving a first order differential inequality, for nontrivial solutions of ℒ u = V u to have a finite order...

From h to p Efficiently: Selecting the Optimal Spectral/hp Discretisation in Three Dimensions

C. D. Cantwell, S. J. Sherwin, R. M. Kirby, P. H. J. Kelly (2011)

Mathematical Modelling of Natural Phenomena

There is a growing interest in high-order finite and spectral/hp element methods using continuous and discontinuous Galerkin formulations. In this paper we investigate the effect of h- and p-type refinement on the relationship between runtime performance and solution accuracy. The broad spectrum of possible domain discretisations makes establishing a performance-optimal selection non-trivial. Through comparing the runtime of different implementations...

From pseudodifferential analysis to modular form theory

André Unterberger (1999)

Journées équations aux dérivées partielles

Taking advantage of methods originating with quantization theory, we try to get some better hold - if not an actual construction - of Maass (non-holomorphic) cusp-forms. We work backwards, from the rather simple results to the mostly devious road used to prove them.

Front d'onde analytique et décomposition microlocale des distributions

Pascal Laubin (1983)

Annales de l'institut Fourier

On étudie en détail une décomposition microlocale analytique de la distribution δ ( x - y ) suivant des distributions singulières en un seul point et dans une seule codirection. Cette décomposition est obtenue à partir d’opérateurs Fourier-Intégraux à phases complexes.On utilise ensuite cet outil pour démontrer le théorème de décomposition du front d’onde analytique des distributions. On établit également des théorèmes concernant la représentation globale des distributions comme sommes de valeurs au bord...

Front propagation for nonlinear diffusion equations on the hyperbolic space

Hiroshi Matano, Fabio Punzo, Alberto Tesei (2015)

Journal of the European Mathematical Society

We study the Cauchy problem in the hyperbolic space ℍ n ( n ≥ 2 ) for the semilinear heat equation with forcing term, which is either of KPP type or of Allen-Cahn type. Propagation and extinction of solutions, asymptotical speed of propagation and asymptotical symmetry of solutions are addressed. With respect to the corresponding problem in the Euclidean space ℝ n new phenomena arise, which depend on the properties of the diffusion process in ℍ n . We also investigate a family of travelling wave solutions, named...

Full discretization of some reaction diffusion equation with blow up

Geneviève Barro, Benjamin Mampassi, Longin Some, Jean Ntaganda, Ousséni So (2006)

Open Mathematics

This paper aims at the development of numerical schemes for nonlinear reaction diffusion problems with a convection that blows up in a finite time. A full discretization of this problem that preserves the blow - up property is presented as well as a numerical simulation. Efficiency of the method is derived via a numerical comparison with a classical scheme based on the Runge Kutta scheme.

Full regularity of bounded solutions to nondiagonal parabolic systems of two equations

Dmitry Portnyagin (2008)

Applicationes Mathematicae

Hölder continuity and, basing on this, full regularity and global existence of weak solutions is studied for a general nondiagonal parabolic system of nonlinear differential equations with the matrix of coefficients satisfying special structure conditions and depending on the unknowns. A technique based on estimating a certain function of unknowns is employed to this end.

Fully adaptive multiresolution schemes for strongly degenerate parabolic equations in one space dimension

Raimund Bürger, Ricardo Ruiz, Kai Schneider, Mauricio Sepúlveda (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

We present a fully adaptive multiresolution scheme for spatially one-dimensional quasilinear strongly degenerate parabolic equations with zero-flux and periodic boundary conditions. The numerical scheme is based on a finite volume discretization using the Engquist-Osher numerical flux and explicit time stepping. An adaptive multiresolution scheme based on cell averages is then used to speed up the CPU time and the memory requirements of the underlying finite volume scheme, whose first-order...

Currently displaying 301 – 320 of 372