共查询到20条相似文献,搜索用时 406 毫秒
1.
Alessandra Lunardi 《Journal of Differential Equations》1985,58(2):228-242
Local and global existence and uniqueness for strict solutions of abstract quasilinear parabolic equations are studied. Applications to quasilinear parabolic partial differential equations are also given. 相似文献
2.
Hermano Frid 《Bulletin of the Brazilian Mathematical Society》2001,32(1):1-35
In this paper we survey recent results on the decay of periodic and almost periodic solutions of conservation laws. We also recall some recent results on the global existence of periodic solutions of conservation laws systems which lie inBV
loc
and are constructed through Glimm scheme. The latter motivates a discussion on a possible strategy for solving the open problem of the global existence of periodic solutions of the Euler equations for nonisentropic gas dynamics. We base our decay analysis on a general result about space-time functions which are almost periodic in the space variable, established here for the first time. This result is an abstract version of Theorem 2.1 in [31], which in turn is an extention of the combined result given by Theorems 3.1–3.2 in [9]. 相似文献
3.
In this paper we establish a geometric theory for abstract quasilinear parabolic equations. In particular, we study existence,
uniqueness, and continuous dependence of solutions. Moreover, we give conditions for global existence and establish smoothness
properties of solutions. The results are based on maximal regularity estimates in continuous interpolation spaces. An important
new ingredient is that we are able to show that quasilinear parabolic evolution equations generate a smooth semiflow on the
trace spaces associated with maximal regularity, which are the natural phase spaces in this framework.
Received August 10, 2000; accepted September 20, 2000. 相似文献
4.
Adrian Constantin Joachim Escher 《NoDEA : Nonlinear Differential Equations and Applications》2006,13(1):91-118
We present some results on the global existence of classical solutions for quasilinear parabolic equations with nonlinear
dynamic boundary conditions in bounded domains with a smooth boundary. 相似文献
5.
本文讨论了一类拟线性抛物型方程初边值问题整体解的存在性和衰减估计.所得结果改进并推广了文献[1]的相应结果. 相似文献
6.
Mark Krasnosel'Skii Reinhard Mennicken Dmitrii Rachinskii 《Mathematische Nachrichten》1999,207(1):133-155
We study quasilinear elliptic equations with strong nonlinear terms and systems of such equations. The methods developed by the authors in [1], [2] are used to prove the existence of solutions for boundary—value problems using some information on behavior of potential bounds for nonlinearities; the L–characteristics of elliptic operators and their fractional powers play an important role. New conditions are suggested for the existence of classical solutions of quasilinear second order elliptic equations. 相似文献
7.
Cung The Anh Tran Dinh Ke 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(2):195-212
In this paper we consider the initial boundary value problem for a class of quasilinear parabolic equations involving weighted
p-Laplacian operators in an arbitrary domain, in which the conditions imposed on the non-linearity provide the global existence,
but not uniqueness of solutions. The long-time behavior of the solutions to that problem is considered via the concept of
global attractor for multi-valued semiflows. The obtained results recover and extend some known results related to the p-Laplacian equations. 相似文献
8.
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
9.
研究了一类具有非线性源项和粘性项的拟线性抛物型方程组的初边值问题.通过构造稳定集, 证明了此问题整体解的存在性, 并建立了解的长时间行为.同时在放松函数的适当假设条件下, 得到了初始能量非负时解的爆破性质及解的生命区间估计. 相似文献
10.
Giovanni Vidossich 《Journal of Differential Equations》1976,21(2):263-278
This paper studies the “internal structure” of the periodic solutions of differential equations with the aim of stating when they are constant functions. Yorke [21] and Lasota and Yorke [10] are the first works which show the existence, uńder certain conditions, of a lower bound for the period of non-constant solutions. As applications of the general results proved in Section 1 we obtain a negative solution to an open problem of Browder, the discovery that the periodic solutions ensured by Vidossich [17, Theorem 3.16], are constant functions, and conditions under which the periodic solutions of hyperbolic and parabolic equations are constant functions. Finally, we note that Li [11] applies the results of Section 1 to differential equations with delay.Various result of this paper point out a strong connection between the existence of periodic solutions of small period of x′ = f(x) and the fact that the origin belongs to the range of f. This situation is explored in [19]. 相似文献
11.
C.V. Pao 《Journal of Mathematical Analysis and Applications》2005,304(2):423-450
This paper is concerned with the existence, stability, and global attractivity of time-periodic solutions for a class of coupled parabolic equations in a bounded domain. The problem under consideration includes coupled system of parabolic and ordinary differential equations, and time delays may appear in the nonlinear reaction functions. Our approach to the problem is by the method of upper and lower solutions and its associated monotone iterations. The existence of time-periodic solutions is for a class of locally Lipschitz continuous reaction functions without any quasimonotone requirement using Schauder fixed point theorem, while the stability and attractivity analysis is for quasimonotone nondecreasing and mixed quasimonotone reaction functions using the monotone iterative scheme. The results for the general system are applied to the standard parabolic equations without time delay and to the corresponding ordinary differential system. Applications are also given to three Lotka-Volterra reaction diffusion model problems, and in each problem a sufficient condition on the reaction rates is obtained to ensure the stability and global attractivity of positive periodic solutions. 相似文献
12.
Taeko Yamazaki 《Mathematical Methods in the Applied Sciences》2009,32(15):1893-1918
We consider a hyperbolic–parabolic singular perturbation problem for a quasilinear hyperbolic equation of Kirchhoff type with dissipation weak in time. The purpose of this paper is to give time‐decay convergence estimates of the difference between the solutions of the hyperbolic equation above and those of the corresponding parabolic equation, together with the unique existence of the global solutions of the hyperbolic equation above. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
13.
This paper is concerned with a system of nonlinear partial differential equations, in short, the coupled Cahn-Hilliard equations, which consists of a fourth order quasilinear parabolic equation and a second order quasilinear parabolic equation. This system was recently derived by Penrose and Fife and also by Alt and Pawlow to describe the non-isothermal phase separation of a two-component system. The global existence and uniqueness of classical solutions is proved. The results about the asymptotic behavior, as time goes to infinity, of solution and about the existence and multiplicity of solutions to the corresponding stationary problem, which is a nonlinear boundary value problem involving nonlocal term and constraints, are also obtained. 相似文献
14.
S. Carl 《Journal of Differential Equations》2003,191(1):206-233
In this paper we consider an initial boundary value problem for a parabolic inclusion whose multivalued nonlinearity is characterized by Clarke's generalized gradient of some locally Lipschitz function, and whose elliptic operator may be a general quasilinear operator of Leray-Lions type. Recently, extremality results have been obtained in case that the governing multivalued term is of special structure such as, multifunctions given by the usual subdifferential of convex functions or subgradients of so-called dc-functions. The main goal of this paper is to prove the existence of extremal solutions within a sector of appropriately defined upper and lower solutions for quasilinear parabolic inclusions with general Clarke's gradient. The main tools used in the proof are abstract results on nonlinear evolution equations, regularization, comparison, truncation, and special test function techniques as well as tools from nonsmooth analysis. 相似文献
15.
Hiromichi Hashimoto 《Journal of Differential Equations》2007,237(2):491-525
We consider a hyperbolic-parabolic singular perturbation problem for a quasilinear equation of Kirchhoff type, and obtain parameter-dependent time decay estimates of the difference between the solutions of a quasilinear dissipative hyperbolic equation of Kirchhoff type and the corresponding quasilinear parabolic equation. For this purpose we show time decay estimates for hyperbolic-parabolic singular perturbation problem for linear equations with a time-dependent coefficient. 相似文献
16.
17.
In this paper the authors investigate the boundedness and almost
periodicity of solutions of semilinear parabolic equations with
boundary degeneracy. The equations may be weakly degenerate or
strongly degenerate on the lateral boundary. The authors prove the
existence, uniqueness and global exponential stability of bounded
entire solutions, and also establish the existence theorem of almost
periodic solutions if the data are almost periodic. 相似文献
18.
19.
1 IntroductionIn this paper we study globaJ solutions to the initiaLboundary value prob1em for quasilinearwave equations with viscosity and a nonlinear perterbation of the fOrmwhere fl is a bounded domain in RN with smooth boundarY afl, and the norilineax termsa(vp), g(u) axe like a(vp) = (l + )vlP)--'/P(P > 1), g(u) =--ju1"u.This problem describes the motion of fixed membrane with strong viscosity. The globalexistence and stability Of smooth solutions fOr one space dimensional case N = 1… 相似文献
20.
E. P. Belan 《Ukrainian Mathematical Journal》1997,49(1):9-24
We prove the existence of an m-parameter family of global solutions of a system of difference-differential equations. For difference-differential equations on a torus, we introduce the notion of rotation number. We also consider the problem of perturbation of an invariant torus of a system of difference-differential equations and study the problem of the existence of periodic and quasiperiodic solutions of second-order difference-differential equations. 相似文献