共查询到20条相似文献,搜索用时 10 毫秒
1.
The goal of this paper is to study the asymptotic behavior of the solution of the quasilinear parabolic boundary value problems defined on cylindrical domains when one or several directions go to infinity. We show that the dimension of the space can be reduced and the rate of convergence is analyzed. The evolution p-Laplacian equations and the generalized heat problems are considered. 相似文献
2.
3.
Monica Marras Stella Vernier-Piro 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,56(6):942-956
The authors study a class of initial boundary value problems associated with parabolic quasilinear equations: by introducing
special auxiliary functions, upper and lower solutions are obtained, which turn out to be sharp in the sense that they coincide
with the solution in particular situations.
To Larry Payne on the occasion of his 80th birthday.
Received: February 3, 2004; revised: April 26, 2004
Partially supported by University of Cagliari 相似文献
4.
We present an approach for proving the global existence of classical solutions of certain quasilinear parabolic systems with homogeneous Dirichlet boundary conditions in bounded domains with a smooth boundary. 相似文献
5.
Vasilii V. Kurta 《Archiv der Mathematik》2005,85(6):563-571
We obtain a new comparison principle for weak solutions of the Cauchy problem for a wide class of quasilinear parabolic inequalities.
This is a nonlinear result with no analogue in linear theory.
Received: 13 January 2005 相似文献
6.
Kai-Seng Chou Shi-Zhong Du Gao-Feng Zheng 《Calculus of Variations and Partial Differential Equations》2007,30(2):251-275
The global, weak solutions for the semilinear problem (1) introduced in Ni-Sacks-Tavantzis (J. Differ. Eq. 54, 97–120 (1984)) are studied. Estimates on the Hausdorff dimension of their singular sets are found. As an application, it
is shown that these solutions must blow up in finite time and become regular eventually when the nonlinearity is supercritical
and the domain is convex. 相似文献
7.
L. E. Payne G. A. Philippin A. Safoui 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(5):750-765
In this paper, we establish continuous dependence inequalities for the solutions u(x, t) of a class of nonlinear parabolic initial-boundary value problems and their gradients when the data are subject to variations.
Dedicated to Joseph Hersch on the occasion of his 80th birthday
(Received: February 24, 2005; revised: March 14, 2005) 相似文献
8.
Vasilii V. Kurta 《Archiv der Mathematik》2006,87(4):368-374
We generalize and improve recent non-existence results for global solutions to the Cauchy problem for the inequality
as well as for the equation ut = Δu + |u|q in the half-space
.
Received: 16 September 2005 相似文献
9.
Nguyen Manh Hung 《Journal of Differential Equations》2008,245(7):1801-1818
The purpose of this paper is to establish the well-posedness and the regularity of solutions of the initial-boundary value problems for general higher order parabolic equations in infinite cylinders with the bases containing conical points. 相似文献
10.
Kevin McLeod Albert Milani 《NoDEA : Nonlinear Differential Equations and Applications》1996,3(1):79-114
We prove that the quasilinear parabolic initial-boundary value problem (1.1) below is globally well-posed in a class of high order Sobolev solutions, and that these solutions possess compact, regular attractors ast+. 相似文献
11.
Kai-Seng Chou Ying-Chuen Kwong 《Calculus of Variations and Partial Differential Equations》2001,12(3):281-315
Three classes of quasilinear parabolic equations which have the common feature that their principal coefficients decay as the solution or its gradient blows up are studied. Long time existence of solutions for their Cauchy problems for initial data with arbitrary growth is established. Received September 9, 1999 / Accepted May 9, 2000 / Published online September 14, 2000 相似文献
12.
We bound the modulus of continuity of solutions to quasilinear parabolic equations in one space variable in terms of the initial modulus of continuity and elapsed time. In particular we characterize those equations for which the Lipschitz constants of solutions can be bounded in terms of their initial oscillation and elapsed time. 相似文献
13.
Michael Pingen 《Archiv der Mathematik》2007,89(4):358-364
We consider bounded, weak solutions of certain quasilinear parabolic systems of second order. If the solution fulfills a suitable
smallness condition, we show that it is H?lder continuous and satisfies an a priori estimate. This is a well known result
of Giaquinta and Struwe [3]. Their argument employs the use of Green’s functions, which is completely avoided in our proof.
Instead, our crucial tool is a weak Harnack inequality for supersolutions due to Trudinger [7] in connection with a technique
developed by L.Caffarelli [1].
Received: 25 September 2006 相似文献
14.
This paper deals with a class of nonlinear parabolic problems in divergence form whose solutions, without appropriate data restrictions, might blow up at some finite time. The purpose of this paper is to establish conditions on the data sufficient to guarantee blow-up of solution at some finite time τ, conditions to ensure that the solution remains bounded as well as conditions to derive some explicit exponential decay bounds for the solution and its derivatives. 相似文献
15.
In this paper, we study the regularity of generalized solutions u(x,t) for the n -dimensional quasi-linear parabolic diffraction problem. By using various estimates and Steklov average methods, we prove that (1): for almost all t the first derivatives ux(x,t) are Hölder continuous with respect to x up to the inner boundary, on which the coefficients of the equation are allowed to be discontinuous; and (2): the first derivative ut(x,t) is Hölder continuous with respect to (x,t) across the inner boundary. 相似文献
16.
In this paper, we study the existence and nonlinear stability of the totally characteristic boundary layer for the quasilinear equations with positive definite viscosity matrix under the assumption that the boundary matrix vanishes identically on the boundary x=0. We carry out a series of weighted estimates to the boundary layer equations—Prandtl type equations to get the regularity and the far field behavior of the solutions. This allows us to perform a weighted energy estimate for the error equation to prove the stability of the boundary layers. The stability result finally implies the asymptotic limit of the viscous solutions. 相似文献
17.
Janusz Mierczyński Wenxian Shen Xiao-Qiang Zhao 《Journal of Differential Equations》2004,204(2):471-510
The purpose of this paper is to investigate uniform persistence for nonautonomous and random parabolic Kolmogorov systems via the skew-product semiflows approach. It is first shown that the uniform persistence of the skew-product semiflow associated with a nonautonomous (random) parabolic Kolmogorov system implies that of the system. Various sufficient conditions in terms of the so-called unsaturatedness and/or Lyapunov exponents for uniform persistence of the skew-product semiflows are then provided. Among others, it is shown that if the associated skew-product semiflow has a global attractor and its restriction to the boundary of the state space has a Morse decomposition which is unsaturated or whose external Lyapunov exponents are positive, then it is uniformly persistent. More specific conditions are discussed for uniform persistence in n-species, particularly 3-species, random competitive systems. 相似文献
18.
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
19.
We study the convergence and decay rate to equilibrium of bounded solutions of the quasilinear parabolic equation
ut−diva(x,∇u)+f(x,u)=0 相似文献
20.
We take up the existence and global behavior of positive continuous solutions of the following nonlinear parabolic equation in (n?2) with boundary conditions u=0 on and u(x,0)=u0(x). The nonlinear term is required to satisfy some conditions related to a functional class , which we introduce in this paper and will be called parabolic Kato class in the half space. Our approach is based on potential theory. 相似文献