共查询到20条相似文献,搜索用时 424 毫秒
1.
A parabolic variational inequality is investigated which comes from the study of the optimal exercise strategy for the perpetual American executive stock options in financial markets. It is a degenerate parabolic variational inequality and its obstacle condition depends on the derivative of the solution with respect to the time variable. The method of discrete time approximation is used and the existence and regularity of the solution are established. 相似文献
2.
We prove that any bounded non-negative solution of a degenerate parabolic problem with Neumann or
mixed boundary conditions converges to a stationary solution. 相似文献
3.
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
4.
Svante Janson 《Journal of Differential Equations》2004,206(1):182-226
In the present paper we find necessary and sufficient conditions on the coefficients of a parabolic equation for convexity to be preserved. A parabolic equation is said to preserve convexity if given a convex initial condition, any solution of moderate growth remains a convex function of the spatial variables for each fixed time. 相似文献
5.
This paper is concerned with a class of quasilinear parabolic and elliptic equations in a bounded domain with both Dirichlet and nonlinear Neumann boundary conditions. The equation under consideration may be degenerate or singular depending on the property of the diffusion coefficient. The consideration of the class of equations is motivated by some heat-transfer problems where the heat capacity and thermal conductivity are both temperature dependent. The aim of the paper is to show the existence and uniqueness of a global time-dependent solution of the parabolic problem, existence of maximal and minimal steady-state solutions of the elliptic problem, including conditions for the uniqueness of a solution, and the asymptotic behavior of the time-dependent solution in relation to the steady-state solutions. Applications are given to some heat-transfer problems and an extended logistic reaction–diffusion equation. 相似文献
6.
Jiaqing Pan 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(15):5069-5080
This work studies the large time behavior of free boundary and continuous dependence on nonlinearity for the Cauchy problem of a degenerate parabolic partial differential equation with absorption. Our objective is to give an explicit expression of speed of propagation of the solution and to show that the solution depends on the nonlinearity of the equation continuously. 相似文献
7.
Monotonicity of solutions and blow-up for
semilinear parabolic equations with nonlinear memory 总被引:2,自引:0,他引:2
We show the existence of monotone in time solutions for
a semilinear parabolic equation with memory. The blow-up rate
estimate of the solution is known to be a consequence of the
monotonicity property. 相似文献
8.
LiShenghong 《高校应用数学学报(英文版)》2000,15(3):297-301
In this paper,the application of the G class of functions in the parabolic class is considered. The regularity of the solution for the first boundary value problem of parabolic equation in divergence form is proved. 相似文献
9.
Juraj Húska Peter Poláčik Mikhail V. Safonov 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2007
We consider the Dirichlet problem for linear nonautonomous second order parabolic equations with bounded measurable coefficients on bounded Lipschitz domains. Using a new Harnack-type inequality for quotients of positive solutions, we show that each positive solution exponentially dominates any solution which changes sign for all times. We then examine continuity and robustness properties of a principal Floquet bundle and the associated exponential separation under perturbations of the coefficients and the spatial domain. 相似文献
10.
Shota Sato 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(4):1383-1392
We consider the Cauchy problem for a parabolic partial differential equation with a power nonlinearity. Our concern in this paper is the existence of a singular solution with smooth initial data. By using the Haraux-Weissler equation, it is shown that there exist singular forward self-similar solutions. Using this result, we also obtain a sufficient condition for the singular solution with general initial data including smooth initial data. 相似文献
11.
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
12.
Liu Zhenhai 《Periodica Mathematica Hungarica》1996,33(3):197-205
In the paper existence results for degenerate quasilinear parabolic initial boundary value problems of higher order are proved.
The weak solution is sought in a suitable weighted Sobolev space using the generalized degree theory.
Supported by the funds of State Educational Commission of China for returned scholars from abroad. 相似文献
13.
We consider a factorization of the non-stationary Schr?dinger operator based on the parabolic Dirac operator introduced by
Cerejeiras, K?hler and Sommen. Based on the fundamental solution for the parabolic Dirac operators, we shall construct appropriated
Teodurescu and Cauchy-Bitsadze operators. Afterwards we will describe how to solve the nonlinear Schr?dinger equation using
Banach fixed point theorem. 相似文献
14.
This paper concerns the uniqueness of the bounded solution to a strongly degenerate parabolic problem. The equation considered may have two kinds of strong degeneracies and there is no restriction on the relation between the two degeneracies. By using Holmgren’s approach, we prove that the bounded solution of the associated initial–boundary value problem is unique under some essentially necessary condition on the growth of the convection. 相似文献
15.
Tor A. Kwembe Zhenbu Zhang 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(6):3078-3091
In this paper, we consider a weak coupled semilinear parabolic system with general Wentzell boundary condition. We prove the well-posedness of the problem and derive different conditions in terms of the powers of the nonlinear terms under which the global solution exists and finite time blow-up occurs. 相似文献
16.
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
17.
In this paper, we study a quasilinear nonuniform parabolic system modelling chemotaxis and taking the volume-filling effect into account. The results on the existence of a unique global classical solution was obtained in Cie?lak (2007) [4]. However, the convergence to equilibrium was not considered in that paper. In this paper, we first obtain the crucial uniform boundedness of the solution. Then with the help of a suitable non-smooth Simon-?ojasiewicz approach we obtain the results on convergence to equilibrium and the decay rate. 相似文献
18.
L.E. Payne 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(4):971-1014
This paper deals with the blow-up of the solution to a semilinear second-order parabolic equation with nonlinear boundary conditions. It is shown that under certain conditions on the nonlinearities and data, blow-up will occur at some finite time and when blow-up does occur upper and lower bounds for the blow-up time are obtained. 相似文献
19.
Mildly degenerate Kirchhoff equations with weak dissipation: Global existence and time decay 总被引:1,自引:0,他引:1
Marina Ghisi 《Journal of Differential Equations》2010,248(2):381-402
We consider the hyperbolic-parabolic singular perturbation problem for a degenerate quasilinear Kirchhoff equation with weak dissipation. This means that the coefficient of the dissipative term tends to zero when t→+∞.We prove that the hyperbolic problem has a unique global solution for suitable values of the parameters. We also prove that the solution decays to zero, as t→+∞, with the same rate of the solution of the limit problem of parabolic type. 相似文献
20.
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