共查询到20条相似文献,搜索用时 0 毫秒
1.
Ali Bentrad 《Journal of Differential Equations》2011,250(9):3652-3667
We give an explicit representation of the solutions of the Cauchy problem, in terms of series of hypergeometric functions, for the following class of partial differential equations with double characteristic at the origin:
(xkt∂+ax∂)(xkt∂+bx∂)u+cxk−1t∂u=0, 相似文献
2.
Rossella Agliardi 《Bulletin des Sciences Mathématiques》2002,126(6):435-444
We consider p-evolution equations with real characteristics. We give a condition, on the lower order terms, that is sufficient for well-posedness of the Cauchy problem in Sobolev spaces. 相似文献
3.
G. M. Henkin 《Journal of Fixed Point Theory and Applications》2007,1(2):239-291
Large time asymptotic structure for solutions of the Cauchy problem for a generalized Burgers equation is determined. In particular,
Gelfand’s question about location of viscous shock waves for such equations is answered. 相似文献
4.
Yachun Li Dongmei Feng Zejun Wang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,56(2):239-253
We are concerned with global entropy solutions to the relativistic Euler equations for a class of large initial data which involve the interaction of shock waves and rarefaction waves. We first carefully analyze the global behavior of the shock curves, the rarefaction wave curves, and their corresponding inverse curves in the phase plane. Based on these analyses, we use the Glimm scheme to construct global entropy solutions to the relativistic Euler equations for the class of large discontinuous initial data.Received: May 23, 2004 相似文献
5.
Ermanno Lanconelli 《Journal of Differential Equations》2010,248(9):2329-2367
We axiomatically develop a potential analysis for a general class of hypoelliptic diffusion equations under the following basic assumptions: doubling condition and segment property for an underlying distance and Gaussian bounds of the fundamental solution. Our analysis is principally aimed to obtain regularity criteria and uniform boundary estimates for the Perron-Wiener solution to the Dirichlet problem. As an example of application, we also derive an exterior cone criterion of boundary regularity and scale-invariant Harnack inequality and Hölder estimate for an important class of operators in non-divergence form with Hölder continuous coefficients, modeled on Hörmander vector fields. 相似文献
6.
Global solutions of the nonlinear magnetohydrodynamic (MHD) equations with general
large initial data are investigated. First the existence and uniqueness of global solutions are
established with large initial data in
H
1.
It is shown that neither shock waves nor vacuum and
concentration are developed in a finite time, although there is a complex interaction between the
hydrodynamic and magnetodynamic effects. Then the continuous dependence of solutions upon
the initial data is proved. The equivalence between the well-posedness problems of the system
in Euler and Lagrangian coordinates is also showed. 相似文献
7.
The paper considers the Cauchy problem for linear partial differential equations of non-Kowalevskian type in the complex domain. It is shown that if the Cauchy data are entire functions of a suitable order, the problem has a formal solution which is multisummable. The precise bound of the admissible order of entire functions is described in terms of the Newton polygon of the equation. 相似文献
8.
This paper furthers the study of Adhikari et al. (2010) [2] on the global regularity issue concerning the 2D Boussinesq equations with vertical dissipation and vertical thermal diffusion. It is shown here that the vertical velocity v of any classical solution in the Lebesgue space Lq with 2?q<∞ is bounded by C1q for C1 independent of q. This bound significantly improves the previous exponential bound. In addition, we prove that, if v satisfies , then the associated solution of the 2D Boussinesq equations preserve its smoothness on [0,T]. In particular, implies global regularity. 相似文献
9.
In this work, we analyze the discrete in time 3D system for the globally modified Navier-Stokes equations introduced by Caraballo (2006) [1]. More precisely, we consider the backward implicit Euler scheme, and prove the existence of a sequence of solutions of the resulting equations by implementing the Galerkin method combined with Brouwer’s fixed point approach. Moreover, with the aid of discrete Gronwall’s lemmas we prove that for the time step small enough, and the initial velocity in the domain of the Stokes operator, the solution is H2 uniformly stable in time, depends continuously on initial data, and is unique. Finally, we obtain the limiting behavior of the system as the parameter N is big enough. 相似文献
10.
In this paper, we study the smoothness effect of Cauchy problem for the spatially homogeneous Landau equation in the hard potential case and the Maxwellian molecules case. We obtain the analytic smoothing effect for the solutions under rather weak assumptions on the initial datum. 相似文献
11.
Ling-Jun Wang 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(10):3314-3328
In this work we study the Gevrey regularity of solutions to a general class of second order quasi-linear equations. Under some kind of sub-ellipticity conditions, we obtain the Gevrey regularity of weak solutions to these equations. 相似文献
12.
Yuanfei LiYan Liu Changhao Lin 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(13):4399-4417
In this paper, we establish the spatial decay bounds for homogeneous Boussinesq equations in a semi-infinite pipe flow. Assuming that the entrance velocity and magnetic field data are restricted appropriately, and it converges to laminar flow as the distance down the pipe tends to infinity, we derive a second order differential inequality that leads to an exponential decay estimate for the energy E(z,t) defined in (27). We also indicate how to establish the explicit bound for the total energy. 相似文献
13.
Songzhe Lian 《Journal of Differential Equations》2008,244(5):1178-1209
For , the author studies the existence of a kind of weak solution to the Cauchy problem
14.
We study the blowing-up behavior of solutions of a class of nonlinear integral equations of Volterra type that is connected with parabolic partial differential equations with concentrated nonlinearities. We present some analytic results and, in the case of the kernel of Abel-kind with power nonlinearity and fixed initial data, we give a numerical approximation by using one-point collocation methods. 相似文献
15.
Giuseppe Da Prato Hélène Frankowska 《NoDEA : Nonlinear Differential Equations and Applications》2006,12(4):481-501
In this paper we consider a stochastic flow in Rn which leaves a closed convex set K invariant. By using a recent characterization of the invariance, involving the distance function, we study the corresponding
transition semigroup Pt and its infinitesimal generator N. Due to the invariance property, N is a degenerate elliptic operator. We study existence of an invariant measure ν of Pt and the realization of N in L2 (H, ν). 相似文献
16.
F. Rezakhanlon 《Probability Theory and Related Fields》1996,104(1):97-146
Summary We study one dimensional particle systems in which particles travel as independent random walks and collide stochastically. The collision rates are chosen so that each particle experiences finitely many collisions per unit time. We establish the kinetic limit and derive the discrete Boltzmann equation for the macroscopic particle density. 相似文献
17.
We are concerned with entropy solutions of the 2×2 relativistic Euler equations for perfect fluids in special relativity. We establish the uniqueness of Riemann solutions in the class of entropy solutions in L∞∩BVloc with arbitrarily large oscillation. Our proof for solutions with large oscillation is based on a detailed analysis of global behavior of shock curves in the phase space and on special features of centered rarefaction waves in the physical plane for this system. The uniqueness result does not require specific reference to any particular method for constructing the entropy solutions. Then the uniqueness of Riemann solutions yields their inviscid large-time stability under arbitrarily largeL1∩L∞∩BVloc perturbation of the Riemann initial data, as long as the corresponding solutions are in L∞ and have local bounded total variation that allows the linear growth in time. We also extend our approach to deal with the uniqueness and stability of Riemann solutions containing vacuum in the class of entropy solutions in L∞ with arbitrarily large oscillation. 相似文献
18.
Yong Zhou 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(3):384-392
In this paper we establish a Serrin’s type regularity criterion on the gradient of pressure for weak solutions to the Navier–Stokes
equations in
It is proved that if the gradient of pressure belongs to Lα, γ with
then the weak solution actually is regular and unique.
Received: May 4, 2004 相似文献
19.
In this paper we study some criteria for the full (space-time) regularity of weak
solutions to the Navier-Stokes equations. In particular, we generalize some
classical and very recent criteria involving the velocity, or its
derivatives. More specifically, we show with elementary tools that if a weak
solution, or its vorticity, is small in appropriate Marcinkiewicz spaces, then it
is regular. 相似文献
20.
Stokes flow between corrugated plates in microdomains has been analyzed using a perturbation method. This approach used the incompressible Navier-Stokes equations, but the velocity-slip is present along the solid-fluid interface. For the slip flow regime, if we introduce Knudsen number (K
n) herein, 0.01 K
n 0.1, the total flow rate is increasing as a ratio of 1 + 6K
nto no-slip Stokes flow. If we consider fixedK
ncases, the corrugations still decrease the flow rate, consideringO(2) terms, and the decrease is maximum as the phase shift becomes 180 °. 相似文献