共查询到20条相似文献,搜索用时 31 毫秒
1.
Mohammadhossein Heidari Sureshjani Shahab Gerami Mohammad Ali Emadi 《Transport in Porous Media》2012,93(1):147-169
One of the widely used methods for modeling matrix–fracture fluid exchange in naturally fractured reservoirs is dual porosity
approach. In this type of modeling, matrix blocks are regarded as sources/sinks in the fracture network medium. The rate of
fluid transfer from matrix blocks into fracture medium may be modeled using shape factor concept (Warren and Root, SPEJ 3:245–255,
1963); or the rate–time solution is directly derived for the specific matrix geometry (de Swaan, SPEJ 16:117–122, 1976). Numerous works have been conducted to study matrix–fracture fluid exchange for slightly compressible fluids (e.g. oil).
However, little attention has been taken to systems containing gas (compressible fluid). The objective of this work is to
develop explicit rate–time solutions for matrix–fracture fluid transfer in systems containing single phase gas. For this purpose,
the governing equation describing flow of gas from matrix block into fracture system is linearized using pseudopressure and
pseudotime functions. Then, the governing equation is solved under specific boundary conditions to obtain an implicit relation
between rate and time. Since rate calculations using such an implicit relation need iterations, which may be computationally
inconvenient, an explicit rate–time relation is developed with the aid of material balance equation and several specific assumptions.
Also, expressions are derived for average pseudopressure in matrix block. Furthermore, simplified solutions (originated from
the complex general solutions) are introduced applicable in infinite and finite acting flow periods in matrix. Based on the
derived solutions, expressions are developed for shape factor. An important observation is that the shape factor for gas systems
is the same as that of oil bearing matrix blocks. Subsequently, a multiplier is introduced which relates rate to matrix pressure
instead of matrix pseudopressure. Finally, the introduced equations are verified using a numerical simulator. 相似文献
2.
Igor Chueshov Irena Lasiecka Daniel Toundykov 《Journal of Dynamics and Differential Equations》2009,21(2):269-314
The paper addresses long-term behavior of solutions to a damped wave equation with a critical source term. The dissipative
frictional feedback is restricted to a subset of the boundary of the domain. This paper derives inverse observability estimates which extend the results of Chueshov et al. (Disc Contin
Dyn Syst 20:459–509, 2008) to systems with boundary dissipation. In particular, we show that a hyperbolic flow under a critical source and geometrically constrained boundary damping approaches a smooth finite-dimensional global attractor. A similar result for subcritical sources was given in Chueshov et al. (Commun Part Diff Eq 29:1847–1876, 2004). However, the criticality of the source term in conjunction
with geometrically restricted dissipation constitutes the major new difficulty of the problem. To overcome this issue we develop
a special version of Carleman’s estimates and apply them in the context of abstract results on dissipative dynamical systems.
In contrast with the localized interior damping (Chueshov et al. Disc Contin Dyn Syst 20:459–509, 2008), the analysis of a
boundary feedback requires a more careful treatment of the trace terms and special tangential estimates based on microlocal analysis.
相似文献
3.
Lu Li 《Journal of Dynamics and Differential Equations》2009,21(4):623-630
The Cauchy problem for the 1D real-valued viscous Burgers equation u
t
+uu
x
= u
xx
is globally well posed (Hopf in Commun Pure Appl Math 3:201–230, 1950). For complex-valued solutions finite time blow-up
is possible from smooth compactly supported initial data, see Poláčik and Šverák (J Reine Angew Math 616:205–217, 2008). It
is also proved in Poláčik and Šverák (J Reine Angew Math 616:205–217, 2008) that the singularities for the complex-valued
solutions are isolated if they are not present in the initial data. In this paper we study the singularities in more detail.
In particular, we classify the possible blow-up rates and blow-up profiles. It turns out that all singularities are of type
II and that the blow-up profiles are regular steady state solutions of the equation. 相似文献
4.
Concerning to the non-stationary Navier–Stokes flow with a nonzero constant velocity at infinity, just a few results have
been obtained, while most of the results are for the flow with the zero velocity at infinity. The temporal stability of stationary
solutions for the Navier–Stokes flow with a nonzero constant velocity at infinity has been studied by Enomoto and Shibata
(J Math Fluid Mech 7:339–367, 2005), in L
p
spaces for p ≥ 3. In this article, we first extend their result to the case
\frac32 < p{\frac{3}{2} < p} by modifying the method in Bae and Jin (J Math Fluid Mech 10:423–433, 2008) that was used to obtain weighted estimates for the Navier–Stokes flow with the zero velocity at infinity. Then, by using
our generalized temporal estimates we obtain the weighted stability of stationary solutions for the Navier–Stokes flow with
a nonzero velocity at infinity. 相似文献
5.
In a previous work, we have shown that chitosan true physical gelation occurs in some organic and inorganic acids (Hamdine et al. 2004). Two systems presenting similar gelation mechanisms were characterized furthermore in order to investigate the sol–gel transition: the chitosan–phosphoric acid and the chitosan–oxalic acid systems. By performing rheological measurements in the framework of linear viscoelasticity, we have investigated the effect of time, temperature, and polymer concentration on the gelation evolution. For both acid-based systems, gelation occurred above a critical polymer concentration around 5% w/v (g/100 ml) of chitosan. Isothermal time sweep experiments showed that the gelation occurs in three stages: (i) incubation; (ii) rapid increase of G′; and (iii) a last stage where G′ slowly reached its equilibrium value due to slow molecular diffusion. At the gel point, G′ and G′′ scaled with ω
n
, with n=0.55 for both acid-based systems and a fractal dimension d
f of 1.9. Cooling–heating cycles revealed that the gels showed thermoreversibility after one sequence, but became permanent during subsequent cycles.This revised version was published online in October 2005 with corrections to the author's name. 相似文献
6.
On the basis of the developed abstract theory of random attractors of probability dissipative systems, we investigate the
qualitative behavior of solutions of a nonuniquely solvable reaction-diffusion equation perturbed by a stochastic “cadlag”
process.
__________
Translated from Neliniini Kolyvannya, Vol. 8, No. 2, pp. 174–185, April–June, 2005. 相似文献
7.
A.V. Vel’hach 《Nonlinear Oscillations》2009,12(1):19-26
We establish sufficient conditions for systems of nonlinear functional differential equations of neutral type to have solutions
that are continuously differentiable and bounded for t ∈ ℝ (together with their first derivatives) and investigate the asymptotic properties of these solutions.
Translated from Neliniini Kolyvannya, Vol. 12, No. 1, pp. 20–26, January–March, 2009. 相似文献
8.
Qionglei Chen Changxing Miao Zhifei Zhang 《Archive for Rational Mechanics and Analysis》2010,195(2):561-578
In this paper, we prove the local well-posedness for the ideal MHD equations in the Triebel–Lizorkin spaces and obtain a blow-up
criterion of smooth solutions. Specifically, we fill a gap in a step of the proof of the local well-posedness part for the
incompressible Euler equation in Chae (Comm Pure Appl Math 55:654–678 2002). 相似文献
9.
In this paper, we establish analyticity of the Navier–Stokes equations with small data in critical Besov spaces . The main method is Gevrey estimates, the choice of which is motivated by the work of Foias and Temam (Contemp Math 208:151–180, 1997). We show that mild solutions are Gevrey regular, that is, the energy bound holds in , globally in time for p < ∞. We extend these results for the intricate limiting case p = ∞ in a suitably designed E ∞ space. As a consequence of analyticity, we obtain decay estimates of weak solutions in Besov spaces. Finally, we provide a regularity criterion in Besov spaces. 相似文献
10.
Using a generalization of the numerical-analytic method, we establish sufficient conditions for the existence of solutions
of systems of partial differential equations with integral condition.
Translated from Neliniini Kolyvannya, Vol. 12, No. 1, pp. 110–119, January–March, 2009. 相似文献
11.
Boris Haspot 《Journal of Mathematical Fluid Mechanics》2011,13(2):223-249
This work is devoted to proving existence of global weak solutions for a general isothermal model of capillary fluids derived
by Dunn and Serrin (Arch Rational Mech Anal 88(2):95–133, 1985) which can be used as a phase transition model. We improve
the results of Danchin and Desjardins (Annales de l’IHP, Analyse non linéaire 18:97–133, 2001) by showing the existence of
global weak solution in dimension two for initial data in the energy space, close to a stable equilibrium and with specific
choices on the capillary coefficients. In particular we are interested in capillary coefficients approximating a constant
capillarity coefficient κ. To finish we show the existence of global weak solution in dimension one for a specific type of capillary coefficients with
large initial data in the energy space. 相似文献
12.
Classification and unfoldings of 1:2 resonant Hopf Bifurcation 总被引:3,自引:0,他引:3
Victor G. LeBlanc William F. Langford 《Archive for Rational Mechanics and Analysis》1996,136(4):305-357
In this paper, we study the bifurcations of periodic solutions from an equilibrium point of a differential equation whose
linearization has two pairs of simple pure imaginary complex conjugate eigenvalues which are in 1:2 ratio. This corresponds
to a Hopf-Hopf mode interaction with 1:2 resonance, as occurs in the context of dissipative mechanical systems. Using an approach
based on Liapunov-Schmidt reduction and singularity theory, we give a framework in which to study these problems and their
perturbations in two cases: no distinguished parameter, and one distinguished (bifurcation) parameter. We give a complete
classification of the generic cases and their unfoldings.
(Accepted May 26, 1995) – Communicated by M. Golubitsky 相似文献
13.
In this work, we are concerned with the regularities of the solutions to the Boltzmann equation with physical collision kernels
for the full range of intermolecular repulsive potentials, r
−(p−1) with p > 2. We give new and constructive upper and lower bounds for the collision operator in terms of standard weighted fractional
Sobolev norms. As an application, we get the global entropy dissipation estimate which is a little stronger than that described
by Alexandre et al. (Arch Rational Mech Anal 152(4):327–355, 2000). As another application, we prove the smoothing effects for the strong solutions constructed by Desvillettes and Mouhot (Arch Rational Mech Anal 193(2):227–253, 2009) of the spatially homogeneous Boltzmann equation with “true” hard potential and “true” moderately soft potential. 相似文献
14.
Daniel N. Riahi 《Transport in Porous Media》2008,72(1):121-138
We consider the problem of mixed oscillatory and steady modes of nonlinear compositional convection in horizontal mushy layers
during the solidification of binary alloys. Under a near-eutectic approximation and the limit of large far-field temperature,
we determine a number of two- and three-dimensional weakly nonlinear mixed solutions, and the stability of these solutions
with respect to arbitrary three-dimensional disturbances is then investigated. The present investigation is an extension of
the problem of mixed oscillatory and steady modes of convection, which was investigated by Riahi (J Fluid Mech 517: 71–101,
2004), where some calculated results were inaccurate due to the presence of a singular point in the equation for the linear
frequency. Here we resolve the problem and find some significant new results. In particular, over a wide range of the parameter
values, we find that the properties of the preferred and stable solution in the form of particular subcritical mixed standing
and steady hexagons appeared to be now in much better agreement with the available experimental results (Tai et al., Nature
359:406–408, 1992) than the one reported in Riahi (J Fluid Mech 517:71–101, 2004). We also determined a number of new types
of preferred supercritical solutions, which can be preferred over particular values of the parameters and at relatively higher
values of the amplitude of convection. 相似文献
15.
John G. Heywood 《Journal of Mathematical Fluid Mechanics》2011,13(3):449-457
Current proofs of time independent energy bounds for solutions of the time dependent Navier–Stokes equations, and of bounds
for the Dirichlet norms of steady solutions, are dependent upon the construction of an extension of the prescribed boundary
values into the domain that satisfies the inequality (1.1) below, for a value of κ less than the kinematic viscosity. It is known from the papers of Leray (J Math Pure Appl 12:1–82, 1993), Hopf (Math Ann
117:764–775, 1941) and Finn (Acta Math 105:197–244, 1961) that such a construction is always possible if the net flux of the
boundary values across each individual component of the boundary is zero. On the other hand, the nonexistence of such an extension,
for small values of κ, has been shown by Takeshita (Pac J Math 157:151–158, 1993) for any two or three-dimensional annular domain, when the boundary
values have a net inflow toward the origin across each component of the boundary. Here, we prove a similar result for boundary
values that have a net outflow away from the origin across each component of the boundary. The proof utilizes a class of test
functions that can detect and measure deformation. It appears likely that much of our reasoning can be applied to other multiply
connected domains. 相似文献
16.
In this article, we study the large time behavior of solutions of first-order Hamilton–Jacobi Equations set in a bounded domain
with nonlinear Neumann boundary conditions, including the case of dynamical boundary conditions. We establish general convergence
results for viscosity solutions of these Cauchy–Neumann problems by using two fairly different methods: the first one relies
only on partial differential equations methods, which provides results even when the Hamiltonians are not convex, and the
second one is an optimal control/dynamical system approach, named the “weak KAM approach”, which requires the convexity of
Hamiltonians and gives formulas for asymptotic solutions based on Aubry–Mather sets. 相似文献
17.
We give a new classification of fixed times of pulse action (uniform, functional, limiting, and quantitatively limiting).
Several results obtained earlier for oscillatory systems with uniform and limiting times of pulse action are generalized to
similar systems with functional times of pulse action. Namely, we obtain estimates, which are exact with respect to a small
parameter ε, for the deviation of solutions and their partial derivatives for original and averaged initial-value, boundary-value,
and multipoint problems.
__________
Translated from Neliniini Kolyvannya, Vol. 9, No. 1, pp. 68–84, January–March, 2006. 相似文献
18.
Germán A. Enciso Morris W. Hirsch Hal L. Smith 《Journal of Dynamics and Differential Equations》2008,20(1):115-132
Classical results in the theory of monotone semiflows give sufficient conditions for the generic solution to converge toward
an equilibrium or toward the set of equilibria (quasiconvergence). In this paper, we provide new formulations of these results
in terms of the measure-theoretic notion of prevalence, developed in Christensen (Israel J. Math., 13, 255–260, 1972) and Hunt et al. (Bull. Am. Math. Soc., 27, 217–238, 1992). For monotone reaction–diffusion systems with Neumann boundary conditions on convex domains, we show the
prevalence of the set of continuous initial conditions corresponding to solutions that converge to a spatially homogeneous
equilibrium. We also extend a previous generic convergence result to allow its use on Sobolev spaces. Careful attention is
given to the measurability of the various sets involved. 相似文献
19.
This paper is concerned with the decay structure for linear symmetric hyperbolic systems with relaxation. When the relaxation
matrix is symmetric, the dissipative structure of the systems is completely characterized by the Kawashima–Shizuta stability
condition formulated in Umeda et al. (Jpn J Appl Math 1:435–457, 1984) and Shizuta and Kawashima (Hokkaido Math J 14:249–275, 1985) and we obtain the asymptotic stability result together with the explicit time-decay rate under that stability condition.
However, some physical models which satisfy the stability condition have non-symmetric relaxation term (for example, the Timoshenko
system and the Euler–Maxwell system). Moreover, it had been already known that the dissipative structure of such systems is
weaker than the standard type and is of the regularity-loss type (see Duan in J Hyperbolic Differ Equ 8:375–413, 2011; Ide et al. in Math Models Meth Appl Sci 18:647–667, 2008; Ide and Kawashima in Math Models Meth Appl Sci 18:1001–1025, 2008; Ueda et al. in SIAM J Math Anal 2012; Ueda and Kawashima in Methods Appl Anal 2012). Therefore our purpose in this paper is to formulate a new structural condition which includes the Kawashima–Shizuta condition,
and to analyze the weak dissipative structure for general systems with non-symmetric relaxation. 相似文献
20.
In this short note we consider the 3D Navier–Stokes equations in the whole space, for an incompressible fluid. We provide
sufficient conditions for the regularity of strong solutions in terms of certain components of the velocity gradient. Based
on the recent results from Kukavica (J Math Phys 48(6):065203, 2007) we show these conditions as anisotropic regularity criteria
which partially interpolate results from Kukavica (J Math Phys 48(6):065203, 2007) and older results of similar type from
Penel and Pokorny (Appl Math 49(5):483–493, 2004). 相似文献