共查询到20条相似文献,搜索用时 15 毫秒
1.
Meng Xu 《Journal of Mathematical Analysis and Applications》2007,325(1):636-654
In this paper we establish the existence and uniqueness of weak solutions for the initial-boundary value problem of a fourth-order nonlinear parabolic equation. 相似文献
2.
Hideo Deguchi 《Monatshefte für Mathematik》2009,156(3):211-231
This paper is devoted to the study of the initial value problem for parabolic systems with discontinuous nonlinearities from
the viewpoint of the existence, uniqueness and stability of weak solutions. Also the relationship with the solutions of the
corresponding differential inclusions is studied.
相似文献
3.
In this paper, the authors study an initial and boundary value problem to a system of evolution p-Laplacian equations coupled with general nonlinear terms. The authors use the method of regularization to construct a sequence of approximation solutions with the help of monotone iteration technique and hence obtain the existence of solutions to a regularized system of equations. Then the existence of solutions to the system of evolution p-Laplacian equations is obtained with the use of a standard limiting process. The uniqueness of the solution is also proven. 相似文献
4.
Existence, uniqueness and asymptotic behavior of solutions for a singular parabolic equation 总被引:2,自引:0,他引:2
In this paper, we are concerned with a singular parabolic equation in a smooth bounded domain Ω⊂RN subject to zero Dirichlet boundary condition and initial condition φ?0. Under the assumptions on μ, φ and f(x,t), some existence and uniqueness results are obtained by applying parabolic regularization method and the sub-supersolutions method. We also discuss the asymptotic behaviors of solutions in the sense of and L∞(0,T;L2(Ω)) norms as μ→0 or μ→∞. As a byproduct we obtain the existence of solutions for some problems which blow up on the boundary. 相似文献
5.
Jinghua Wang 《Journal of Differential Equations》2003,189(1):1-16
In this paper, we study a generalized Burgers equation ut+(u2)x=tuxx, which is a non-uniformly parabolic equation for t>0. We show the existence and uniqueness of classical solutions to the initial-value problem of the generalized Burgers equation with rough initial data belonging to . 相似文献
6.
Matej Kordoš 《Journal of Mathematical Analysis and Applications》2004,298(2):655-666
We consider the system
7.
Zhou Wen-Shu 《Journal of Mathematical Analysis and Applications》2008,346(1):107-119
In this paper we study existence and multiplicity of weak solutions of the homogenous Dirichlet problem for a singular semilinear elliptic equation with a quadratic gradient term. The proofs for the main results are based on a priori estimates of solutions of approximate problems. 相似文献
8.
This paper is devoted to studying the existence and asymptotic behavior of solutions to a nonlinear parabolic equation of fourth order: ut+∇⋅(|∇Δu|p−2∇Δu)=f(u) in Ω⊂RN with boundary condition u=Δu=0 and initial data u0. The substantial difficulty is that the general maximum principle does not hold for it. The solutions are obtained for both the steady-state case and the developing case by the fixed point theorem and the semi-discretization method. Unlike the general procedures used in the previous papers on the subject, we introduce two families of approximate solutions with determining the uniform bounds of derivatives with respect to the time and space variables, respectively. By a compactness argument with necessary estimates, we show that the two approximation sequences converge to the same limit, i.e., the solution to be determined. In addition, the decays of solutions towards the constant steady states are established via the entropy method. Finally, it is interesting to observe that the solutions just tend to the initial data u0 as p→∞. 相似文献
9.
Dragos-Patru Covei 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(5):2684-4168
This paper deals with the existence and uniqueness of a positive solution to the semilinear elliptic equation of the Lane, Emden and Fowler type. 相似文献
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In this paper, we present some general results of existence and uniqueness of solutions of nonlinear two-point boundary value problems for third-order nonlinear differential equations by using the Shooting method. As applications we give certain concrete sufficient conditions for the existence and uniqueness. 相似文献
13.
In this paper, we consider a kind of Rayleigh equation with finitely many deviating arguments of the form
14.
宋斌恒 《应用数学学报(英文版)》1994,10(2):113-140
EXISTENCE,UNIQUENESSANDPROPERTIESOFTHESOLUTIONSOFADEGENERATEPARABOLICEQUATIONWITHDIFFUSION-ADVECTION-ABSORPTION¥SONGBINHENG(宋... 相似文献
15.
Zhaoyong Feng 《Journal of Mathematical Analysis and Applications》2010,368(1):235-246
In this paper, we establish the existence and uniqueness of weak solutions for the initial-boundary value problem of a class of generalized nonlinear parabolic partial differential equations, which are related to the Malik-Perona model in image analysis. 相似文献
16.
D. D. Hai 《Proceedings of the American Mathematical Society》2005,133(1):223-228
We obtain necessary and sufficient conditions for the existence of positive solutions for a class of sublinear Dirichlet quasilinear elliptic systems.
17.
Jinghua Wang 《Journal of Mathematical Analysis and Applications》2003,284(1):213-235
In this paper we study the generalized Burgers equation ut+(u2/2)x=f(t)uxx, where f(t)>0 for t>0. We show the existence and uniqueness of classical solutions to the initial value problem of the generalized Burgers equation with rough initial data belonging to , as well it is obtained the decay rates of u in Lp norm are algebra order for p∈[1,∞[. 相似文献
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19.
We prove the global existence and uniqueness of admissible weak solutions to an asymptotic equation of a nonlinear hyperbolic variational wave equation with nonnegative L 2(ℝ) initial data. The work of Ping Zhang is supported by the Chinese postdoctor’s foundation, and that of Yuxi Zheng is supported in part by NSF DMS-9703711 and the Alfred P. Sloan Research Fellows award. 相似文献
20.
M. Kanakaraj 《Proceedings Mathematical Sciences》1998,108(2):169-177
A class of evolution integrodifferential equation has been studied over the analytic semigroup of operators in a Banach space.
Further the existence of weak and strong solutions in Banach space have been proved and extended to a maximum interval of
existence. 相似文献