共查询到20条相似文献,搜索用时 15 毫秒
1.
Donatella Donatelli Konstantina Trivisa 《Archive for Rational Mechanics and Analysis》2007,185(3):379-408
We consider a multidimensional model for the combustion of compressible reacting fluids. The flow is governed by the Navier–Stokes
in Eulerian coordinates and the chemical reaction is irreversible and is governed by the Arrhenius kinetics. The existence
of globally defined weak solutions is established by using weak convergence methods, compactness and interpolation arguments
in the spirit of Feireisl [16] and P.L. Lions [24]. 相似文献
2.
This work is concerned with the time discrete analysis of the Oseen system of equations driven by nonlinear slip boundary conditions of friction type. We study the existence of solutions of the time discrete model and derive several a priori estimates needed to recover the solution of the continuous problem by means of weak compactness. Moreover, for the difference between the exact and approximate solutions, we obtain the rate of convergence of order one with respect to the time step without imposing extra regularity on the weak solution. 相似文献
3.
Stéphane Mischler 《Archive for Rational Mechanics and Analysis》1997,140(1):53-77
In this paper we prove the convergence of two discrete-velocity deterministic schemes for the Boltzmann equation, namely,
Buet's scheme and a new finite-volume scheme that we introduce here. We write the discretized equation in the form of a Boltzmann
continuous equation in order to be in the framework of the DiPerna-Lions theory of renormalized solutions. In order to prove
convergence we have to overcome two difficulties: the convergence of the discretized collision kernel is very weak and the
lemma on the compactness of velocity averages can be recovered only asymptotically when the parameter of discretization tends
to zero.
(Accepted February 6, 1996) 相似文献
4.
George Noel Djoufedie Elisabetta Felaco Bruno Rubino Rosella Sampalmieri 《Continuum Mechanics and Thermodynamics》2016,28(1-2):331-349
This paper is devoted to the compactness framework and the convergence theorem for the Lax–Friedrichs and Godunov schemes applied to a \({2 \times 2}\) system of non-strictly hyperbolic nonlinear conservation laws that arises from mathematical models for oil recovery. The presence of a degeneracy in the hyperbolicity of the system requires a careful analysis of the entropy functions, whose regularity is necessary to obtain the result. For this purpose, it is necessary to combine the classical techniques referring to a singular Euler–Poisson–Darboux equation with the compensated compactness method. 相似文献
5.
In this paper a compactness framework for approximate solutions to nonlinear hyperbolic systems with umbilic degeneracy is established by combining techniques of compensated compactness with some classical methods, and by a detailed analysis of a highly singular equation of Euler-Poisson-Darboux type. Then this framework is successfully applied to prove the convergence of the viscosity method and to prove the existence of global entropy solutions for the Cauchy problem with large initial data for a canonical class of the systems with quadratic flux form. 相似文献
6.
Gui-Qiang Chen Fei-Min Huang Tian-Yi Wang 《Archive for Rational Mechanics and Analysis》2016,219(2):719-740
A compactness framework is established for approximate solutions to subsonic-sonic flows governed by the steady full Euler equations for compressible fluids in arbitrary dimension. The existing compactness frameworks for the two-dimensional irrotational case do not directly apply for the steady full Euler equations in higher dimensions. The new compactness framework we develop applies for both non-homentropic and rotational flows. One of our main observations is that the compactness can be achieved by using only natural weak estimates for the mass balance and the vorticity, along with the Bernoulli law and the entropy relation, through a more delicate analysis on the phase space. As direct applications, we establish two existence theorems for multidimensional subsonic-sonic full Euler flows through infinitely long nozzles. 相似文献
7.
Wen Huang Danylo Khilko Sergiĭ Kolyada Alfred Peris Guohua Zhang 《Journal of Dynamics and Differential Equations》2018,30(3):1221-1245
Dynamical compactness with respect to a family as a new concept of chaoticity of a dynamical system was introduced and discussed in Huang et al. (J Differ Equ 260(9):6800–6827, 2016). In this paper we continue to investigate this notion. In particular, we prove that all dynamical systems are dynamically compact with respect to a Furstenberg family if and only if this family has the finite intersection property. We investigate weak mixing and weak disjointness by using the concept of dynamical compactness. We also explore further difference between transitive compactness and weak mixing. As a byproduct, we show that the \(\omega _{{\mathcal {F}}}\)-limit and the \(\omega \)-limit sets of a point may have quite different topological structure. Moreover, the equivalence between multi-sensitivity, sensitive compactness and transitive sensitivity is established for a minimal system. Finally, these notions are also explored in the context of linear dynamics. 相似文献
8.
殷朝阳 《应用数学和力学(英文版)》1997,18(9):913-919
I.Introducti0nlnthearticle,wemainlydiscussthefollowingequations:wherej(.)isasmoothnonlinearmapfromRtoR,l'l2andlI'if2.denotethenormofH'(R)andthenormofL'"(R),respectively,C0isaconstant.Asdandsgotozero,theconvergenceandregularityforthesolutionsofEq.(l.l)andE… 相似文献
9.
We continue to study hyperbolic systems of conservation laws with umbilic degeneracy. We further extend our compactness framework established earlier to other canonical classes of quadratic flux systems with an isolated umbilic point. With the aid of this compactness framework, we establish the compactness of solution operators and the long-time behavior of entropy solutions in L ∞ with large initial data, and we prove the convergence of the viscosity method, as well as the Lax-Friedrichs scheme and the Godunov scheme, for a canonical class of nonlinear hyperbolic systems with umbilic degeneracy. 相似文献
10.
João Paulo Dias Mário Figueira Hermano Frid 《Archive for Rational Mechanics and Analysis》2010,196(3):981-1010
Motivated by Benney’s general theory, we propose new models for short wave–long wave interactions when the long waves are
described by nonlinear systems of conservation laws. We prove the strong convergence of the solutions of the vanishing viscosity
and short wave–long wave interactions systems by using compactness results from compensated compactness theory and new energy
estimates obtained for the coupled systems. We analyze several of the representative examples, such as scalar conservation
laws, general symmetric systems, nonlinear elasticity and nonlinear electromagnetism. 相似文献
11.
Zakharov equations have a fairly abundant physical background. In this paper, the existence of the weak global solution for
quantum Zakharov equations for the plasmas model is obtained by means of the Arzela-Ascoli theorem, Faedo-Galerkin methods,
and compactness property. 相似文献
12.
Existence of global weak solutions to the continuous coagulation-fragmentation equations with diffusion is investigated when the kinetic coefficients satisfy a detailed balance condition or the coagulation coefficient enjoys a monotonicity condition. Our approach relies on weak and strong compactness methods in L 1 in the spirit of the DiPerna-Lions theory for the Boltzmann equation. Under the detailed balance condition the large-time behaviour is also studied. 相似文献
13.
Pablo Pedregal 《Archive for Rational Mechanics and Analysis》2010,197(3):965-983
We introduce a certain property for a continuous (non-linear) operator that allows for the existence of critical points for
functionals when the derivative complies with such a condition, without the need to check either weak lower semicontinuity
or convexity. This condition is formulated in terms of Young measures, and so it requires restricting attention to true spaces
of functions. It turns out that this property is a generalization of the standard compactness for a continuous, non-linear
operator. We illustrate the relevance of this condition by applying it to the solution of typical Cauchy problems for ODEs,
as well as boundary-value problems in one space dimension, and defer the much more complicated situation of PDEs in higher
dimensions for a later work. 相似文献
14.
丁协平 《应用数学和力学(英文版)》1999,20(10):1087-1098
IntroductionVariationalinequalitytheoryandcomplementarityproblemtheoryhavebecomeveryeffectiveandpowerfultoolsforstudyingawiderangeofproblemsarisinginmechanics,mathematicalprogramming,optimizationandcontrol,equilibriumtheoryofeconomics,managementscien… 相似文献
15.
A. Azarkhin 《Journal of Elasticity》1985,15(3):233-241
Suppose that a given complicated domain is constructed from two or more partially overlapping subdomains, for which solutions are available. The convergence in energy of the iterative method that reduces the given problem to a sequence of problems for simple subdomains is proved. Properties of Sobolev's spaces are employed, namely the theorem on equivalent norms and compactness of a bounded set.Aluminum Company of America, formerly at the University of MichiganProduct Engineering Div., ALCOA Laboratories, ALCOA CenterProduct Engineering Div., ALCOA Laboratories, ALCOA Center 相似文献
16.
IntroductionInthispaper,westudytheunsteadyaxisymmetricincompressibleflowbetweentwoconcentricspheres.Thisflowiscalledasspheric... 相似文献
17.
凌镛镛 《应用数学和力学(英文版)》1992,13(3):273-279
In the present paper the concept and properties of the residual functional in Sobolev space are investigated. The weak compactness,
force condition, lower semi-continuity and convex of the residual functional are proved. In Sobolev space, the minimum principle
of the residual functional is proposed. The minimum existence theoreom for J(u)=0 is given by the modern critical point theory.
And the equivalence theorem or five equivalence forms for the residual functional equation are also proved. 相似文献
18.
J. R. Cannon Emmanuele DiBenedetto George H. Knightly 《Archive for Rational Mechanics and Analysis》1980,73(1):79-97
For steady-state Stefan problems with convection in the fluid phase governed by either the Stokes equations or the Navier Stokes equations, and with adherence of the fluid on all boundaries, the existence of a weak solution is obtained via the introduction of a temperature dependent penalty term in the fluid flow equation together with application of various compactness arguments.This research was supported in part by the National Science Foundation and the Consiglio Nazionale delle Ricerche. 相似文献
19.
凌镛镛 《应用数学和力学(英文版)》1992,(3)
In the present paper the concept and properties of the residual functional in Sobolev space are investigated. The weak compactness, force condition, lower semi-continuity and convex of the residual functional are proved. In Sobolev space, the minimum principle of the residual functional is proposed. The minimum existence theoreom for J(u)=0 is given by the modern critical point theory. And the equivalence theorem or five equivalence forms for the residual functional equation are also proved. 相似文献
20.
Prof. G. Toscani 《Continuum Mechanics and Thermodynamics》1992,4(2):95-107
We give a new proof of convergence towards equilibrium for a gas of Maxwellian pseudo-molecules with finite mass, momentum and energy. No entropy is needed for weak * convergence. Strong convergence follows in the case of planar velocities by a suitable use of theJ-functional introduced by McKean for the Kac's caricature of the Maxwellian gas. 相似文献