共查询到20条相似文献,搜索用时 0 毫秒
1.
A. A. Alikhanov 《Differential Equations》2010,46(5):660-666
We consider boundary value problems of the first and third kind for the diffusionwave equation. By using the method of energy
inequalities, we find a priori estimates for the solutions of these boundary value problems. 相似文献
2.
Gerhard Kristensson Niklas Wellander 《Mathematical Methods in the Applied Sciences》2015,38(11):2194-2215
In this paper, we present a collection of a priori estimates of the electromagnetic field scattered by a general bounded domain. The constitutive relations of the scatterer are in general anisotropic. Surface averages are investigated, and several results on the decay of these averages are presented. The norm of the exterior Calderón operator for a sphere is investigated and depicted as a function of the frequency. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
3.
Ya. Belopolskaya 《Journal of Mathematical Sciences》1998,92(6):4256-4272
A class of nondiagonal systems of nonlinear parabolic equations that can be reduced to a scalar parabolic equation in the
phase space of a larger dimension is described. In view of such a reduction, it is possible to state the maximum principle
for solutions to systems of nonlinear parabolic equations and derive a priori C2+α-estimates for a solution to the Cauchy problem. Bibliography: 19 titles.
Translated fromProblemy Matematicheskogo Analiza, No. 16. 1997, pp. 41–67. 相似文献
4.
Markus Biegert 《manuscripta mathematica》2010,133(3-4):273-306
The purpose of this paper is to prove a priori estimates for the difference of weak solutions to certain quasi-linear elliptic equations, where the p(x)-Laplace operator serves as a prototype for our method. 相似文献
5.
Ar. S. Tersenov 《Siberian Mathematical Journal》2012,53(3):539-550
Under consideration is the Dirichlet problem for singular anisotropic elliptic equations with a nonlinear source. Some new a priori estimates are obtained, implying that the solvability of the Dirichlet problem in the class of bounded solutions essentially depends on the dimension of the domain of the problem. 相似文献
6.
A. V. Ivanov 《Journal of Mathematical Sciences》1978,10(2):217-240
We consider classes of elliptic equations of the form (x,u,u
D
2
u)=0 for the solutions of which one establishes local and global a priori estimates for D
2
u=. In particular, one investigates the Monge-Ampere equation, and for its convex solutions one constructs a local and a global estimate for D
2
u and a local estimate for.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 59, pp. 31–59, 1976. 相似文献
7.
8.
9.
CAO Yi LI DongSheng & WANG LiHe College of Science Xi’an Jiaotong University Xi’an China Department of Mathematics The University of Iowa Iowa City IA - USA 《中国科学 数学(英文版)》2011,(3):457-462
For the fully nonlinear uniformly elliptic equation F(D2u) = 0, it is well known that the viscosity solutions are C2,α if the nonlinear operator F is convex (or concave). In this paper, we study the classical solutions for the fully nonlinear elliptic equation where the nonlinear operator F is locally C1,β a.e. for any 0 < β < 1. We will prove that the classical solutions u are C2,α. Moreover, the C2,α norm of u depends on n,F and the continuous modulus of D2u. 相似文献
10.
A. V. Ivanov 《Journal of Mathematical Sciences》1978,10(1):44-53
Local estimates on the boundary of a domain for the gradients of solutions of second-order quasilinear elliptic equations are constructed. These estimates are applied to establish local estimates on the boundary for the second derivatives of solutions of a certain class of second-order nonlinear elliptic equations.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 69, pp. 65–76, 1977. 相似文献
11.
12.
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
13.
Chao-Jiang Xu 《Journal of Differential Equations》2005,210(1):217-231
In this paper, we consider the local existence of solutions to Euler equations with linear damping under the assumption of physical vacuum boundary condition. By using the transformation introduced in Lin and Yang (Methods Appl. Anal. 7 (3) (2000) 495) to capture the singularity of the boundary, we prove a local existence theorem on a perturbation of a planar wave solution by using Littlewood-Paley theory and justifies the transformation introduced in Liu and Yang (2000) in a rigorous setting. 相似文献
14.
M.E Schonbek 《Journal of Mathematical Analysis and Applications》1981,82(2):553-565
In this paper we establish L∞-bounds for the derivatives of all orders of the solutions to the FitzHugh-Nagumo equations, by means of comparison functions. We obtain bounds for the initial value problem, the Dirichlet problem and the Neumann problem. The FitzHugh-Nagumo equations arise in mathematical biology as a model for the conduction of electrical impulses along a nerve axon. 相似文献
15.
The Riemann solutions for the Euler system of conservation laws of energy and momentum in special relativity for polytropic gases are considered. It is rigorously proved that, as pressure vanishes, they tend to the two kinds of Riemann solutions to the corresponding pressureless relativistic Euler equations: the one includes a delta shock, which is formed by a weighted δ-measure, and the other involves vacuum state. 相似文献
16.
G. G. Laptev 《Mathematical Notes》1998,64(4):488-495
We study an initial boundary value problem for the semilinear parabolic equation
where the left-hand side is a linear uniformly parabolic operator of order 2b. We prove sufficient growth conditions on the functionƒ with respect to the variablesu, Du,, D
2b–1
u, such that the apriori estimate of the norm of the solution in the Sobolev spaceW
p
2b,1
is expressible in terms of the low-order norm in the Lebesgue space of integrable functionsL
l,m
.Translated fromMatematicheskie Zametki, Vol. 64, No. 4, pp. 564–572, October, 1998.In conclusion, the author wishes to thank his scientific adviser, corresponding member of the Russian Academy of Sciences S. I. Pokhozhaev, for setting the problem and useful discussions of the results, and also Ya. Sh. Il'yasov for valuable remarks.This research was supported by the Russian Foundation for Basic Research under grant No. 96-15-96102. 相似文献
17.
Yachun Li Dongmei Feng Zejun Wang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,29(6):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. 相似文献
18.
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
19.
20.
Feimin Huang 《Journal of Differential Equations》2006,220(1):207-233
The asymptotic behavior of solutions of the damped compressible Euler equations is conjectured to obey to the famous porous media equations (PMES). The previous works on this topic concern the case away from vacuum where the system is strictly hyperbolic. In present paper, we prove that the L∞ entropy weak solution with vacuum, obtained by the compensated compactness theory, converges strongly in space to the unique similarity solution of the related PME, as time goes to infinity. 相似文献