共查询到20条相似文献,搜索用时 32 毫秒
1.
R. G. Akhmetov 《Differential Equations》2010,46(2):159-166
We consider a class of quasilinear second-order ordinary differential equations that arise in the investigation of the problem
on stationary convective mass transfer between a drop and a solid medium in the presence of a volume chemical reaction of
power-law form [F(υ) ≡ υ
ν
] for the case in which the Peclet number Pe and the rate constant k
υ
of the volume chemical reaction tend to infinity. We prove the existence and uniqueness theorem for a boundary value problem
and analyze asymptotic properties of the solution. 相似文献
2.
Ke WANG 《数学年刊B辑(英文版)》2011,32(6):803-822
Based on the theory of semi-global C
1 solution and the local exact boundary controllability for first-order quasilinear hyperbolic systems, the local exact boundary
controllability for a kind of second-order quasilinear hyperbolic systems is obtained by a constructive method. 相似文献
3.
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
4.
LIUGUOQING 《高校应用数学学报(英文版)》1995,10(4):427-438
A nonlinear difference scheme is given for solving a quasilinear siagularly perturbed two-point boundary value problem with a turning point. The method uses non-equidistant discretization meshes. The solution of the scheme is shown to be first order accurate in the discrete L^∞ norm, uniformly in the perturbation parameter. 相似文献
5.
A. A. Arkhipova 《Journal of Mathematical Sciences》2009,159(4):391-410
A variational problem with an obstacle for a certain class of quadratic functionals is considered. Admissible vector-valued
functions are assumed to satisfy the Dirichlet boundary condition, and the obstacle is a given smooth (N − 1)-dimensional surface S in ℝ
N
. The surface S is not necessarily bounded.
It is proved that any minimizer u of such an obstacle problem is a partially smooth function up to the boundary of a prescribed domain. It is shown that the
(n − 2)-Hausdorff measure of the set of singular points is zero. Moreover, u is a weak solution of a quasilinear system with two kinds of quadratic nonlinearities in the gradient. This is proved by
a local penalty method. Bibliography: 25 titles.
Dedicated to V. A. Solonnikov on the occasion of his jubilee
Published in Zapiski Nauchnykh. Seminarov POMI, Vol. 362, 2008, pp. 15–47. 相似文献
6.
The finite element based approximation of a quasilinear elliptic equation of non monotone type with Neumann boundary conditions
is studied. Minimal regularity assumptions on the data are imposed. The consideration is restricted to polygonal domains of
dimension two and polyhedral domains of dimension three. Finite elements of degree k ≥ 1 are used to approximate the equation. Error estimates are established in the L
2(Ω) and H
1(Ω) norms for convex and non-convex domains. The issue of uniqueness of a solution to the approximate discrete equation is
also addressed. 相似文献
7.
Ke WANG 《数学年刊B辑(英文版)》2016,37(6):803-820
Based on the theory of semi-global classical solutions to quasilinear
hyperbolic systems, the local exact boundary observability for a
kind of second-order quasilinear hyperbolic systems is obtained by a
constructive method. 相似文献
8.
C. A. Stuart 《Milan Journal of Mathematics》2011,79(1):327-341
For a class of second order quasilinear elliptic equations we establish the existence of two non–negative weak solutions of
the Dirichlet problem on a bounded domain, Ω. Solutions of the boundary value problem are critical points of C
1–functional on H01(W){H_0^1(\Omega)}. One solution is a local minimum and the other is of mountain pass type. 相似文献
9.
Shuxing Chen 《Frontiers of Mathematics in China》2007,2(1):87-102
This paper is devoted to initial boundary value problems for quasi-linear symmetric hyperbolic systems in a domain with characteristic
boundary. It extends the theory on linear symmetric hyperbolic systems established by Friedrichs to the nonlinear case. The
concept on regular characteristics and dissipative boundary conditions are given for quasilinear hyperbolic systems. Under
some assumptions, an existence theorem for such initial boundary value problems is obtained. The theorem can also be applied
to the Euler system of compressible flow.
__________
Translated from Chinese Annals of Mathematics, Ser. A, 1982, 3(2): 223–232 相似文献
10.
A. A. Arkhipova 《Journal of Mathematical Sciences》1998,92(6):4231-4255
The Cauchy-Dirichlet problem for quasilinear parabolic systems of second-order equations is considered in the case of two
spatial variables. Under the condition that the corresponding elliptic operator has variational structure, the global in time
solvability is established. The solution is smooth almost everywhere and the number of singular points is finite. Sufficient
conditions that guarantee the absence of singular points are given. Bibliography: 23 titles.
Translated fromProblemy Matematicheskogo Analiza No. 16, 1997, pp. 3–40. 相似文献
11.
H. P. Lopushans’ka 《Ukrainian Mathematical Journal》2007,59(12):1885-1901
We establish conditions for the nonlinear part of a quasilinear elliptic equation of order 2m with linear principal part under which a solution regular inside a domain and belonging to a certain weighted L
1-space takes boundary values in the space of generalized functions.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 12, pp. 1674–1688, December, 2007. 相似文献
12.
Mikhail A. Borodin 《Journal of Mathematical Sciences》2011,178(1):13-40
We prove the existence of a global classical solution of the multidimensional two-phase Stefan problem. The problem is reduced
to a quasilinear parabolic equation with discontinuous coefficients in a fixed domain. With the help of a small parameter
ε, we smooth coefficients and investigate the resulting approximate solution. An analytical method that enables one to obtain
the uniform estimates of an approximate solution in the cross-sections t = const is developed. Given the uniform estimates, we make the limiting transition as ε → 0. The limit of the approximate solution is a classical solution of the Stefan problem, and the free boundary is a surface
of the class H
2+α,1+α/2. 相似文献
13.
Yu. S. Kolesov 《Mathematical Notes》2000,68(2):191-200
We consider a model example of a quasilinear wave equation in the unit square with zero boundary conditions and use the method
of quasinormal forms to prove that there are quite a few dichotomic cycles and tori bifurcating from zero equilibrium. A conjecture
concerning the attractor structure is presented.
Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 217–229, August, 2000. 相似文献
14.
We analyze a class of quasilinear elliptic problems involving a p(·)-Laplace-type operator on a bounded domain
W ì \mathbb RN{\Omega\subset{\mathbb R}^N}, N ≥ 2, and we deal with nonlinear conditions on the boundary. Working on the variable exponent Lebesgue–Sobolev spaces, we
follow the steps described by the “fountain theorem” and we establish the existence of a sequence of weak solutions. 相似文献
15.
For quasilinear equations div A(x, u, ∇u) = 0 with degeneracy ω(x) of the Muckenhoupt A
p
-class, we prove the Harnack inequality, an estimate for the H?lder norm, and a sufficient criterion for the regularity of
boundary points of the Wiener type.
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 7, pp. 918–936, July, 2008. 相似文献
16.
In this paper we develop a geometric theory for quasilinear parabolic problems in weighted L
p
-spaces. We prove existence and uniqueness of solutions as well as the continuous dependence on the initial data. Moreover,
we make use of a regularization effect for quasilinear parabolic equations to study the ω-limit sets and the long-time behaviour of the solutions. These techniques are applied to a free boundary value problem. The
results in this paper are mainly based on maximal regularity tools in (weighted) L
p
-spaces. 相似文献
17.
Hans-Christoph Kaiser Hagen Neidhardt Joachim Rehberg 《NoDEA : Nonlinear Differential Equations and Applications》2006,13(3):287-310
Using results on abstract evolutions equations and recently obtained results on elliptic operators with discontinuous coefficients
including mixed boundary conditions we prove that quasilinear parabolic systems admit a local, classical solution in the space
of p–integrable functions, for some p greater than 1, over a bounded two dimensional space domain. The treatment of such equations in a space of integrable functions
enables us to define the normal component of the current across the boundary of any Lipschitz subset. As applications we have
in mind systems of reaction diffusion equations, e.g. van Roosbroeck’s system. 相似文献
18.
Hui-ling LI & Ming-xin WANG Department of Mathematics Southeast University Nanjing China 《中国科学A辑(英文版)》2007,50(4):590-608
This paper deals with the properties of positive solutions to a quasilinear parabolic equation with the nonlinear absorption and the boundary flux. The necessary and sufficient conditions on the global existence of solutions are described in terms of different parameters appearing in this problem. Moreover, by a result of Chasseign and Vazquez and the comparison principle, we deduce that the blow-up occurs only on the boundary (?)Ω. In addition, for a bounded Lipschitz domainΩ, we establish the blow-up rate estimates for the positive solution to this problem with a= 0. 相似文献
19.
This paper discusses both the nonexistence of positive solutions for second-order three-point boundary value problems when the nonlinear term f(t, x, y) is superlinear in y at y = 0 and the existence of multiple positive solutions for second-order three-point boundary value problems when the nonlinear term f(t, x,y) is superlinear in x at +∞. 相似文献
20.
A priori estimates are established for solutions to initial/boundary-value problems for quasilinear parabolic equations of
nondivergence type with the Venttsel' boundary condition. These estimates are used in proving the existence theorems in Sobolev
spaces. Bibliography: 7 titles.
Translated fromProblemy Matematicheskogo Analiza. No. 15. 1995, pp. 33–46. 相似文献