共查询到20条相似文献,搜索用时 15 毫秒
1.
The main focus in this paper is on homogenization of the parabolic problem ∂
t
uɛ − ∇ · (a(x/ɛ,t/ɛ,t/ɛ
r
)∇u
ɛ
) = f. Under certain assumptions on a, there exists a G-limit b, which we characterize by means of multiscale techniques for r > 0, r ≠ 1. Also, an interpretation of asymptotic expansions in the context of two-scale convergence is made. 相似文献
2.
Huaiyu Jian 《中国科学A辑(英文版)》1999,42(2):133-139
Giorgi conjectured in 1979 that if a sequence of functionals converges in the sense of Г-convergence to a limiting functional, then the corresponding gradient flows will converge as well after changing timescale appropriately. It is shown that this conjecture holds true for a rather wide kind of functionals. Project supported by the National Natural Science Foundation of China (Grant No. 19701018). 相似文献
3.
Guochun Wen 《Communications in Nonlinear Science & Numerical Simulation》2000,5(4):174-178
In this paper the initial-irregular oblique derivative problems for fully nonlinear parabolic equations of second order are proposed, and then some a priori estimates of solutions for the above problems are given. 相似文献
4.
Olivier Baconneau Alessandra Lunardi 《Transactions of the American Mathematical Society》2004,356(3):987-1005
We establish existence, uniqueness, and regularity results for solutions to a class of free boundary parabolic problems, including the free boundary heat equation which arises in the so-called ``focusing problem' in the mathematical theory of combustion. Such solutions are proved to be smooth with respect to time for positive , if the data are smooth.
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Global solutions for quasilinear parabolic problems 总被引:4,自引:0,他引:4
Results on the global existence of classical solutions for quasilinear parabolic equations in bounded domains with homogeneous
Dirichlet or Neumann boundary conditions are presented. Besides quasilinear parabolic equations, the method is also applicable
to some weakly-coupled reaction-diffusion systems and to elliptic equations with nonlinear dynamic boundary conditions.
Received December 21, 2000; accepted August 30, 2001. 相似文献
8.
Fuensanta Andrs Julio Muoz Jesús Rosado 《Mathematical Methods in the Applied Sciences》2019,42(18):6049-6066
This work is a follow‐up to a series of articles by the authors where the same topic for the elliptic case is analyzed. In this article, a class of nonlocal optimal design problem driven by parabolic equations is examined. After a review of results concerning existence and uniqueness for the state equation, a detailed formulation of the nonlocal optimal design is given. The state equation is of nonlocal parabolic type, and the associated cost functional belongs to a broad class of nonlocal integrals. In the first part of the work, a general result on the existence of nonlocal optimal design is proved. The second part is devoted to analyzing the convergence of nonlocal optimal design problems toward the corresponding classical problem of optimal design. After a slight modification of the problem, either on the cost functional or by considering a new set of admissibility, the G‐convergence for the state equation and, consequently, the convergence of the nonlocal optimal design problem are proved. 相似文献
9.
D. Azé 《Mathematical Programming》1988,41(1-3):127-140
Combining the Clarke-Ekeland dual least action principle and the epi-convergence, we state an existence result and study the asymptotic behaviour for the periodic solution of a nonlinear Sturm-Liouville problem deriving from a convex subquadratic potential, when the data are perturbed in a suitable sense. The result appears like a stability result for the minimizers of a sequence of DC functions. 相似文献
10.
E. Grenier 《Journal de Mathématiques Pures et Appliquées》1997,76(10):965-990
In this paper we study boundary layers of nonlinear characteristic parabolic equations as the viscosity goes to zero. We obtain and justify in small time a complete expansion of the solution with respect to the viscosity. 相似文献
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This paper is devoted to the homogenization of a nonlinear degenerate parabolic problem ɑtu∈-div(D(x/∈, u∈,▽u∈)+ K(x/∈, u∈))= f(x) with Dirichlet boundary condition. Here the operator D(y, s,s) is periodic in y and degenerated in ▽s. In the paper, under the two-scale convergence theory, we obtain the limit equation as ∈→ 0 and also prove the corrector results of ▽u∈ to strong convergence. 相似文献
14.
Amin Boumenir 《Mathematical Methods in the Applied Sciences》2017,40(16):5881-5892
We are concerned with the identification and reconstruction of the coefficients of a linear parabolic system from finite time observations of the solution on the boundary. We present two procedures depending on whether the spectrum of the system is simple or multiple. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
15.
Two explicit error representation formulas are derived for degenerate parabolic PDEs, which are based on evaluating a parabolic residual in negative norms. The resulting upper bounds are valid for any numerical method, and rely on regularity properties of solutions of a dual parabolic problem in nondivergence form with vanishing diffusion coefficient. They are applied to a practical space-time discretization consisting of piecewise linear finite elements over highly graded unstructured meshes, and backward finite differences with varying time-steps. Two rigorous a posteriori error estimates are derived for this scheme, and used in designing an efficient adaptive algorithm, which equidistributes space and time discretization errors via refinement/coarsening. A simulation finally compares the behavior of the rigorous a posteriori error estimators with a heuristic approach, and hints at the potentials and reliability of the proposed method.
16.
Massimo Gobbino 《Mathematical Methods in the Applied Sciences》1999,22(5):375-388
We investigate the evolution problem where H is a Hilbert space, A is a self‐adjoint linear non‐negative operator on H with domain D(A), and is a continuous function. We prove that if , and , then there exists at least one global solution, which is unique if either m never vanishes, or m is locally Lipschitz continuous. Moreover, we prove that if for all , then this problem is well posed in H. On the contrary, if for some it happens that for all , then this problem has no solution if with β small enough. We apply these results to degenerate parabolic PDEs with non‐local non‐linearities. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
17.
Fares Mokhtari 《Mathematical Methods in the Applied Sciences》2013,36(2):196-207
In this paper, we prove existence and regularity of weak solutions for a class of nonlinear anisotropic parabolic problems in with locally integrable data. Our approach is based on the anisotropic Sobolev inequality, a smoothness, and compactness results. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
18.
研究了一类带有非线性边界条件的非线性抛物型方程组解的整体存在及解在有限时刻爆破问题.通过构造方程组的上、下解.得到了解整体存在及解在有限时刻爆破的充分条件.对指数型反应项和边界流采用了常微分方程方法构造其上下解,而其它例如第一特征值等方法运用于该方程就比较困难. 相似文献
19.
In this paper the homogenization of degenerate nonlinear parabolic equations where a(t,y,λ) is periodic in (t,y), is studied via a weighted compensated compactness result. 相似文献
20.
Fabio Punzo 《Journal of Differential Equations》2011,251(7):1972-1989
We investigate existence and uniqueness of solutions to semilinear parabolic and elliptic equations in bounded domains of the n-dimensional hyperbolic space (n?3). Lp→Lq estimates for the semigroup generated by the Laplace-Beltrami operator are obtained and then used to prove existence and uniqueness results for parabolic problems. Moreover, under proper assumptions on the nonlinear function, we establish uniqueness of positive classical solutions and nonuniqueness of singular solutions of the elliptic problem; furthermore, for the corresponding semilinear parabolic problem, nonuniqueness of weak solutions is stated. 相似文献