共查询到20条相似文献,搜索用时 0 毫秒
1.
Yann Brenier 《Archive for Rational Mechanics and Analysis》2009,193(1):1-19
We show that Kruzhkov’s theory of entropy solutions to multidimensional scalar conservation laws (Kruzhkov in Mat Sb (N.S.),
81(123), 228–255, 1970) can be entirely recast in L
2 and fits into the general theory of maximal monotone operators in Hilbert spaces. Our approach is based on a combination
of level-set, kinetic and transport-collapse approximations, in the spirit of previous works by Brenier (in C R Acad Sci Paris
Ser I Math, 292, 563–566, 1981; in J Diff Equ, 50, 375–390, 1983; in SIAM J Numer Anal, 21, 1013–1037; in Methods Appl Anal,
11, 515–532, 2004), Giga and Miyakawa (in Duke Math J, 50, 505–515, 1983), and Tsai et al. (in Math Comp, 72, 159–181, 2003). 相似文献
2.
Boris Andreianov Kenneth Hvistendahl Karlsen Nils Henrik Risebro 《Archive for Rational Mechanics and Analysis》2011,201(1):27-86
We propose a general framework for the study of L
1 contractive semigroups of solutions to conservation laws with discontinuous flux:
$ u_t + \mathfrak{f}(x,u)_x=0, \qquad \mathfrak{f}(x,u)= \left\{{ll} f^l(u),& x < 0,\\ f^r(u), & x > 0, \right.\quad\quad\quad (\rm CL) $ u_t + \mathfrak{f}(x,u)_x=0, \qquad \mathfrak{f}(x,u)= \left\{\begin{array}{ll} f^l(u),& x < 0,\\ f^r(u), & x > 0, \end{array} \right.\quad\quad\quad (\rm CL) 相似文献
3.
We prove that nonsmooth quasilinear parabolic systems admit a local solution in L
p
strongly differentiable with respect to time over a bounded three-dimensional polyhedral space domain. The proof rests essentially on new elliptic regularity results for polyhedral Laplace interface problems for anisotropic materials. These results are based on sharp pointwise estimates for Greens function, which are also of independent interest. To treat the nonlinear problem, we then apply a classical theorem of Sobolevskii for abstract parabolic equations and recently obtained resolvent estimates for elliptic operators and interpolation results. As applications we have in mind primarily reaction-diffusion systems. The treatment of such equations in an L
p
context seems to be new and allows (by Gauss theorem) the proper definition of the normal component of currents across the boundary. 相似文献
4.
We study the L
1
stability of multi-dimensional discrete-velocity Boltzmann equations. Under suitable smallness assumption on initial data, we show that bounded mild solutions are L
1
stable. For a stability estimate, we employ Bonys multi-dimensional analysis for total interactions over characteristic planes. 相似文献
5.
We study rates of convergence of solutions in L
2 and H
1/2 for a family of elliptic systems {Le}{\{\mathcal{L}_\varepsilon\}} with rapidly oscillating coefficients in Lipschitz domains with Dirichlet or Neumann boundary conditions. As a consequence,
we obtain convergence rates for Dirichlet, Neumann, and Steklov eigenvalues of {Le}{\{\mathcal{L}_\varepsilon\}} . Most of our results, which rely on the recently established uniform estimates for the L
2 Dirichlet and Neumann problems in Kenig and Shen (Math Ann 350:867–917, 2011; Commun Pure Appl Math 64:1–44, 2011) are new even for smooth domains. 相似文献
6.
We study the L1 stability of classical solutions to the Boltzmann equation for a hard-sphere model, when initial datum is a small perturbation of a vacuum, and tends to zero exponentially fast at infinity in the phase space. For this, we introduce nonlinear functionals measuring potential interactions between particles with different velocities and L1 distance between classical solutions. We use pointwise estimates for a solution and the gain term of a collision operator to control the time-evolution of nonlinear functionals.Dedicated to Marshall Slemrod on the occasion of his 60th birthday 相似文献
7.
In this paper we study the two-dimensional hydrostatic Euler equations in a periodic channel. We prove the local existence
and uniqueness of H
s
solutions under the local Rayleigh condition. This extends Brenier’s (Nonlinearity 12(3):495–512, 1999) existence result by removing an artificial condition and proving uniqueness. In addition, we prove weak–strong uniqueness,
mathematical justification of the formal derivation and stability of the hydrostatic Euler equations. These results are based
on weighted H
s
a priori estimates, which come from a new type of nonlinear cancellation between velocity and vorticity. 相似文献
8.
In this paper, we study the extremals of the curvature energy actions on non-null curves in the four-dimensional Lorentz-Minkowski space. We derive the motion equations and find three Killing fields along the generalized elastic curves. We also construct a cylindrical coordinate system using these Killing fields and express the generalized elastic curves by means of quadratures. 相似文献
9.
10.
11.
We prove the solvability in Sobolev spaces for both divergence and non-divergence form higher order parabolic and elliptic
systems in the whole space, on a half space, and on a bounded domain. The leading coefficients are assumed to be merely measurable
only in the time variable and have small mean oscillations with respect to the spatial variables in small balls or cylinders.
For the proof, we develop a set of new techniques to produce mean oscillation estimates for systems on a half space. 相似文献
12.
A continuous function is said to be infinity harmonic if it satisfies the PDEin the viscosity sense. In this paper we prove that infinity harmonic functions are continuously differentiable when n=2. 相似文献
13.
Stationary Solutions and Connecting Orbits for <Emphasis Type="Italic">p</Emphasis>-Laplace Equation
Aleksander Ćwiszewski Mateusz Maciejewski 《Journal of Dynamics and Differential Equations》2018,30(1):309-329
We deal with one dimensional p-Laplace equation of the form 相似文献
$$\begin{aligned} u_t = (|u_x|^{p-2} u_x )_x + f(x,u), \ x\in (0,l), \ t>0, \end{aligned}$$ 14.
Peter Hornung 《Archive for Rational Mechanics and Analysis》2011,199(3):1015-1067
Let \({S\subset\mathbb{R}^2}\) be a bounded Lipschitz domain and denote by \({W^{2,2}_{\text{iso}}(S; \mathbb{R}^3)}\) the set of mappings \({u\in W^{2,2}(S;\mathbb{R}^3)}\) which satisfy \({(\nabla u)^T(\nabla u) = Id}\) almost everywhere. Under an additional regularity condition on the boundary \({\partial S}\) (which is satisfied if \({\partial S}\) is piecewise continuously differentiable), we prove that the strong W 2,2 closure of \({W^{2,2}_{\text{iso}}(S; \mathbb{R}^3)\cap C^{\infty}(\overline{S};\mathbb{R}^3)}\) agrees with \({W^{2,2}_{\text{iso}}(S; \mathbb{R}^3)}\). 相似文献
15.
肖海滨 《应用数学和力学(英文版)》2010,31(11):1453-1462
This paper addresses the regularity and finite dimensionality of the global attractor for the plate equation on the unbounded domain. The existence of the attractor in the phase space has been established in an earlier work of the author. It is shown that the attractor is actually a bounded set of the phase space and has finite fractal dimensionality. 相似文献
16.
A class of nonlinear elliptic problems driven by p(x)-Laplacian with a nonsmooth locally Lipschitz potential is considered.By applying the version of the nonsmooth three-critical-point theorem,the existence of three solutions to the problems is proved. 相似文献
17.
A single-exponential growth estimate of the solutions to the 2-dimensional Navier–Stokes equations in the whole space for
nondecaying initial velocity is established. The crucial idea is to decompose velocity into high and low frequency parts.
Moreover, if the linear term and the vorticity decay exponentially, the velocity is bounded uniformly in time.
相似文献
18.
The bioluminescence images of unstirred cultures show that lux reporter E. coli (0.10 mg biomass per ml of the broth medium) in 6.4–10 mm diameter circular containers induce center-fluid-rising toroidal
convection of ≤1 mm/min. The bioconvective torus is stable in a Teflon vessel and is deformed by 3.2–4.4 mm wavelength azimuthal
waves in polystyrene or glass vessels. 相似文献
19.
20.
In this article, we study a semilinear p-Laplacian Dirichlet problem arising in population dynamics. We obtain the Morse critical groups at zero. The results show that the energy functional of the problem is trivial. As a consequence, the existence and bifurcation of the nontrivial solutions to the problem are established. 相似文献
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