2,254 research outputs found
Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy
We study the asymptotic time behavior of global smooth solutions to general
entropy dissipative hyperbolic systems of balance law in m space dimensions,
under the Shizuta-Kawashima condition. We show that these solutions approach
constant equilibrium state in the Lp-norm at a rate O(t^(-m/2(1-1/p))), as t
tends to , for p in [min (m,2),+ \infty]. Moreover, we can show that we
can approximate, with a faster order of convergence, theconservative part of
the solution in terms of the linearized hyperbolic operator for m >= 2, and by
a parabolic equation in the spirit of Chapman-Enskog expansion. The main tool
is given by a detailed analysis of the Green function for the linearized
problem
Asymptotic behavior of 2D stably stratified fluids with a damping term in the velocity equation
This article is concerned with the asymptotic behavior of the two-dimensional
inviscid Boussinesq equations with a damping term in the velocity equation.
Precisely, we provide the time-decay rates of the smooth solutions to that
system. The key ingredient is a careful analysis of the Green kernel of the
linearized problem in Fourier space, combined with bilinear estimates and
interpolation inequalities for handling the nonlinearity
Nonresonant bilinear forms for partially dissipative hyperbolic systems violating the Shizuta-Kawashima condition
In the context of hyperbolic systems of balance laws, the Shizuta-Kawashima
coupling condition guarantees that all the variables of the system are
dissipative even though the system is not totally dissipative. Hence it plays a
crucial role in terms of sufficient conditions for the global in time existence
of classical solutions. However, it is easy to find physically based models
that do not satisfy this condition, especially in several space dimensions. In
this paper, we consider two simple examples of partially dissipative hyperbolic
systems violating the Shizuta-Kawashima condition ([SK]) in 3D, such that some
eigendirections do not exhibit dissipation at all. We prove that, if the source
term is non resonant (in a suitable sense) in the direction where dissipation
does not play any role, then the formation of singularities is prevented,
despite the lack of dissipation, and the smooth solutions exist globally in
time. The main idea of the proof is to couple Green function estimates for
weakly dissipative hyperbolic systems with the space-time resonance analysis
for dispersive equations introduced by Germain, Masmoudi and Shatah. More
precisely, the partially dissipative hyperbolic systems violating [SK] are
endowed, in the non-dissipative directions, with a special structure of the
nonlinearity, the so-called Nonresonant Bilinear Form for the wave equation
(see Pusateri and Shatah, CPAM 2013)
The role of environmental policies in promoting venture capital investments in cleantech companies
Efeito de fontes de carbono no crescimento e na composição bioquÃmica das microalgas Chaetoceros muelleri e Thalassiosira fluviatilis, com enfase no teor de ácidos graxos poliinsaturados
Tese (doutorado) - Universidade Federal de Santa Catarina, Centro de Ciências Agrárias, Programa de Pós-Graduação em Ciência dos Alimentos
- …