共查询到20条相似文献,搜索用时 15 毫秒
1.
We obtain existence results for some strongly nonlinear Cauchy problems posed in
and having merely locally integrable data. The equations we deal with have as principal part a bounded, coercive and pseudomonotone
operator of Leray-Lions type acting on
, they contain absorbing zero order terms and possibly include first order terms with natural growth. For any p > 1 and under
optimal growth conditions on the zero order terms, we derive suitable local a-priori estimates and consequent global existence
results. 相似文献
2.
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
3.
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
4.
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
5.
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
6.
Zhaoyang YIN 《NoDEA : Nonlinear Differential Equations and Applications》2006,13(2):235-248
We present a result on the global existence of classical solutions for quasilinear parabolic system in bounded domains with
homogenous Neumann boundary conditions. 相似文献
7.
Blow-up for semilinear parabolic equations with nonlinear memory 总被引:4,自引:0,他引:4
In this paper, we consider the semilinear parabolic
equation
with homogeneous Dirichlet boundary conditions, where
p, q are
nonnegative constants. The blowup criteria and the blowup rate
are obtained. 相似文献
8.
徐龙封 《高校应用数学学报(英文版)》2004,19(3):272-278
In this paper the nonnegative classical solutions of a parabolic system with nonlinear boundary conditions are discussed. The existence and uniqueness of a nonnegative classical solution are proved. And some sufficient conditions to ensure the global existence and nonexistence of nonnegative classical solution to this problem are given. 相似文献
9.
Adrian Constantin 《NoDEA : Nonlinear Differential Equations and Applications》2005,12(3):383-389
We present a result on the global existence of classical solutions for quasilinear parabolic systems with homogeneous Dirichlet
boundary conditions in bounded domains with a smooth boundary. Our method relies on the use of Lyapunov functions. 相似文献
10.
Gianni Gilardi 《Journal of Differential Equations》2006,228(2):707-736
This note addresses the analysis of an abstract doubly nonlinear Volterra equation with a nonsmooth kernel and possibly unbounded and degenerate operators. By exploiting a suitable implicit time-discretization technique, we obtain the existence of a global strong solution. As a by-product, the discrete scheme is proved to be conditionally stable and convergent. 相似文献
11.
Victor N. Starovoitov 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(6):3009-3027
The Dirichlet problem in arbitrary domain for degenerate and singular anisotropic parabolic equations with a nonlinear source term is considered. We state conditions that guarantee the existence and uniqueness of a global weak solution to the problem. A similar result is proved for the parabolic p-Laplace equation. 相似文献
12.
This paper deals with the blow-up of positive solutions for a nonlinear parabolic equation subject to nonlinear boundary conditions. We obtain the conditions under which the solutions may exist globally or blow up in a finite time, by a new approach. Moreover, upper estimates of the “blow-up time”, blow-up rate and global solutions are obtained also. 相似文献
13.
14.
15.
We investigate quasilinear systems of parabolic partial differential equations with fully nonlinear boundary conditions on
bounded or exterior domains in the setting of Sobolev–Slobodetskii spaces. We establish local wellposedness and study the
time and space regularity of the solutions. Our main results concern the asymptotic behavior of the solutions in the vicinity
of a hyperbolic equilibrium. In particular, the local stable and unstable manifolds are constructed.
Dedicated to Giuseppe Da Prato on the occasion of his 70th birthday 相似文献
16.
17.
C.V. Pao 《Journal of Differential Equations》2010,248(5):1175-540
Coupled systems for a class of quasilinear parabolic equations and the corresponding elliptic systems, including systems of parabolic and ordinary differential equations are investigated. The aim of this paper is to show the existence, uniqueness, and asymptotic behavior of time-dependent solutions. Also investigated is the existence of positive maximal and minimal solutions of the corresponding quasilinear elliptic system. The elliptic operators in both systems are allowed to be degenerate in the sense that the density-dependent diffusion coefficients Di(ui) may have the property Di(0)=0 for some or all i=1,…,N, and the boundary condition is ui=0. Using the method of upper and lower solutions, we show that a unique global classical time-dependent solution exists and converges to the maximal solution for one class of initial functions and it converges to the minimal solution for another class of initial functions; and if the maximal and minimal solutions coincide then the steady-state solution is unique and the time-dependent solution converges to the unique solution. Applications of these results are given to three model problems, including a scalar polynomial growth problem, a coupled system of polynomial growth problem, and a two component competition model in ecology. 相似文献
18.
Fengping Yao 《Journal of Differential Equations》2019,266(4):2078-2099
In this paper we obtain the following local Lorentz estimates of the weak solutions for a class of quasilinear parabolic systems where for . 相似文献
19.
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
20.
We study the blow up behaviour of nonlinear parabolic equations including a time degeneracy, under dynamical boundary conditions. For some exponential and polynomial degeneracies, we develop some energy methods and some spectral comparison techniques and derive upper bounds for the blow up times. 相似文献