Search results for "PDE"
showing 10 items of 558 documents
Fractal Weyl law for open quantum chaotic maps
2014
We study the semiclassical quantization of Poincar\'e maps arising in scattering problems with fractal hyperbolic trapped sets. The main application is the proof of a fractal Weyl upper bound for the number of resonances/scattering poles in small domains near the real axis. This result encompasses the case of several convex (hard) obstacles satisfying a no-eclipse condition.
Can there be a general nonlinear PDE theory for existence of solutions ?
2010
Updated version of the 2004 paper arxiv:math/0407026; Contrary to widespread perception, there is ever since 1994 a unified, general type independent theory for the existence of solutions for very large classes of nonlinear systems of PDEs. This solution method is based on the Dedekind order completion of suitable spaces of piece-wise smooth functions on the Euclidean domains of definition of the respective PDEs. The method can also deal with associated initial and/or boundary value problems. The solutions obtained can be assimilated with usual measurable functions or even with Hausdorff continuous functions on the respective Euclidean domains. It is important to note that the use of the or…
Weak Langmuir turbulence in disordered multimode optical fibers
2021
We consider the propagation of temporally incoherent waves in multimode optical fibers (MMFs) in the framework of the multimode nonlinear Schr\"odinger (NLS) equation accounting for the impact of the natural structural disorder that affects light propagation in standard MMFs (random mode coupling and polarization fluctuations). By averaging the dynamics over the fast disordered fluctuations, we derive a Manakov equation from the multimode NLS equation, which reveals that the Raman effect introduces a previously unrecognized nonlinear coupling among the modes. Applying the wave turbulence theory on the Manakov equation, we derive a very simple scalar kinetic equation describing the evolution…
Experimental parabolic pulse generation with an active dispersion decreasing fiber
2008
We experimentally demonstrate the use of an hybrid configuration to generate parabolic pulses. We combine dispersion decrease with distributed gain. This leads to several benefits on the parabolic generated pulses compared with a passive configuration.
Rational solutions to the mKdV equation associated to particular polynomials
2021
International audience; Rational solutions to the modified Korteweg-de Vries (mKdV) equation are given in terms of a quotient of determinants involving certain particular polynomials. This gives a very efficient method to construct solutions. We construct very easily explicit expressions of these rational solutions for the first orders n = 1 until 10.
Compte rendu de : "Elisa Capdevila, Culture, médias, pouvoirs, 1945-1991, Paris, La Documentation photographique, mai 2019"
2019
International audience
Analysis of errors caused by incomplete knowledge of material data in mathematical models of elastic media
2011
Identifiability problem for recovering the mortality rate in an age-structured population dynamics model
2014
In this article is studied the identifiability of the age-dependent mortality rate of the Von Foerster–Mc Kendrick model, from the observation of a given age group of the population. In the case where there is no renewal for the population, translated by an additional homogeneous boundary condition to the Von Foerster equation, we give a necessary and sufficient condition on the initial density that ensures the mortality rate identifiability. In the inhomogeneous case, modelled by a non-local boundary condition, we make explicit a sufficient condition for the identifiability property, and give a condition for which the identifiability problem is ill-posed. We illustrate this latter case wit…
Apdeguma traumas pacientu aprūpe pēc autodermoplastikas
2019
Bakalaura darba tēma – “Apdeguma traumas pacientu aprūpe pēc autodermoplastikas”. Tēmas aktualitāti nosaka apdeguma traumas specifiskā būtība, kura rada ādas bojājumu un viena no pieejamām ārstēšanas metodēm, kad dabīgie šūnu reģenerācijas procesi nespēj tikt galā ar ādas bojāto daļu atjaunošanu, ir operācija – autodermoplastika. Darba mērķis ir analizēt aprūpi pēc autodermoplastikas apdeguma traumas pacientiem. Pētniecības uzdevumi ir analizēt literatūru un informāciju par apdeguma traumu un autodermoplastiku, izstrādāt un veikt interviju, apkopot un analizēt iegūtos datus, izdarīt secinājumus. Pētniecības jautājums: kāda ir aprūpe pēc autodermoplastikas apdeguma traumas pacientiem. Pētnie…
Aprūpes problēmas pacientiem ar termiskām traumām
2016
Bakalaura darba tēma ir “Aprūpes problēmas pacientiem ar termiskām traumām”. Darba mērķis ir noskaidrot un analizēt aprūpes problēmas pacientiem ar termiskām traumām. Pētījuma jautājums ir: kādas ir aprūpes problēmas pacientiem ar termiskām traumām? Tēmas aktualitāti nosaka apdegumu traumu pieaugums, par ko liecina statistiskie dati. Pētnieciskā darba autors analizē un apkopo bakalaura darbam atbilstošus literatūras avotus, analizē M. Levaines māszinību teoriju, izstrādā pētījuma instrumentu – interviju, veic kvalitatīvu datu analīzi par pētījuma iegūtiem datiem. Darba teorētiskā daļā ir apkopots termiskās traumas raksturojums, tās veidi un pakāpes, sarežģījumi (komplikācijas), ka arī iespē…