共查询到20条相似文献,搜索用时 246 毫秒
1.
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
2.
This paper deals with a nonclassical initial boundary value problem for a two dimensional parabolic equation with Bessel operator. We prove the existence and uniqueness of the weak solution of the given nonlinear problem. We start by solving the associated linear problem. After writing this latter in its operator form, we establish an a priori bound from which we deduce the uniqueness of the strong solution. For the solvability of the associated linear problem, we prove that the range of the operator generated by the considered problem is dense. On the basis of the obtained results of the linear problem, we apply an iterative process to establish the existence and uniqueness of the nonlinear problem. 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.
Noriko Mizoguchi 《Journal of Differential Equations》2004,205(2):298-328
This paper is concerned with blowup phenomena of solutions for the Cauchy and the Cauchy-Dirichlet problem of
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5.
Xueli BaiShuangshuang Zhou Sining Zheng 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(7):2508-2514
This paper studies the Cauchy problem for the fast diffusion equation with a localized reaction. We establish the Fujita type theorem to the problem, and then obtain the diffusion-independent blow-up rate for the non-global solutions. Moreover, we prove that the blow-up set for the problem consists of a single point under large initial data. These conclusions are quite different from those for the slow diffusion case. 相似文献
6.
Jiebao Sun Jingxue YinYifu Wang 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(6):2415-2424
This paper is concerned with a doubly degenerate parabolic equation with logistic periodic sources. We are interested in the discussion of the asymptotic behavior of solutions of the initial-boundary value problem. In this paper, we first establish the existence of non-trivial nonnegative periodic solutions by a monotonicity method. Then by using the Moser iterative method, we obtain an a priori upper bound of the nonnegative periodic solutions, by means of which we show the existence of the maximum periodic solution and asymptotic bounds of the nonnegative solutions of the initial-boundary value problem. We also prove that the support of the non-trivial nonnegative periodic solution is independent of time. 相似文献
7.
C.Y. Chan 《Journal of Computational and Applied Mathematics》2011,235(13):3724-3727
A multi-dimensional parabolic first initial-boundary value problem with a concentrated nonlinear source is studied. A criterion for its solution to quench, in a finite time tq, everywhere on the concentrated nonlinear source only is given. An upper bound for tq is also deduced. For illustration, an example is given. 相似文献
8.
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
9.
Tor A. Kwembe 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(10):3162-3170
In this paper we consider a semilinear equation with a generalized Wentzell boundary condition. We prove the local well-posedness of the problem and derive the conditions of the global existence of the solution and the conditions for finite time blow-up. We also derive an estimate for the blow-up time. 相似文献
10.
We consider the Cauchy problem of the heat equation with a potential which behaves like the inverse square at infinity. In this paper we study the large time behavior of hot spots of the solutions for the Cauchy problem, by using the asymptotic behavior of the potential at the space infinity. 相似文献
11.
The author proves the uniqueness of the solution to an evolution Landau–Lifshitz type problem, when the parameter tends to zero. In addition, the unique solution is just a heat flow of a harmonic map. This uniqueness result is derived by establishing a uniform estimate for the solution. 相似文献
12.
Jingxue Yin 《Journal of Differential Equations》2007,237(2):421-445
The paper concerns the well-posedness problem of an evolutionary weighted p-Laplacian with boundary degeneracy. Different from the classical theory for linear equations, it is shown that the degenerate portion of the boundary should be decomposed into two parts: the strongly degenerate boundary on which the equation exhibits hyperbolic characteristics and the weakly degenerate boundary on which the equation still exhibits parabolic characteristics. We formulate reasonably the boundary value condition and establish the existence and uniqueness theorems. 相似文献
13.
Narcisa Apreutesei 《Journal of Computational and Applied Mathematics》2010,235(2):366-379
In this paper we study a prey-predator model defined by an initial-boundary value problem whose dynamics is described by a Holling type III functional response. We establish global existence and uniqueness of the strong solution. We prove that if the initial data are positive and satisfy a certain regularity condition, the solution of the problem is positive and bounded on the domain and then we deduce the continuous dependence on the initial data. A numerical approximation of the system is carried out with a spectral method coupled with the fourth-order Runge-Kutta time solver. The biological relevance of the comparative numerical results is also presented. 相似文献
14.
Noriko Mizoguchi 《Journal of Functional Analysis》2005,220(1):214-227
The present paper is concerned with a Cauchy problem for a semilinear heat equation
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15.
Noriko Mizoguchi 《Journal of Differential Equations》2006,231(1):182-194
The present paper is concerned with a Cauchy problem for a semilinear heat equation
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16.
José-Francisco Rodrigues 《Acta Appl Math》1987,8(1):1-35
Considering the one-phase Stefan problem, we present an account of some recent mathematical results within the framework of variational inequalities. We discuss several situations corresponding to different boundary conditions and different geometries, like the exterior problem, the continuous casting model, and the degenerate case of the quasi-steady model. We develop a few continuous-dependence results explaining their relevance to the stability properties of the solution and of the free boundary, including the asymptotic behaviour for large time, the stability for homogenization, and the perturbation of the Dirichlet boundary conditions. 相似文献
17.
Said Mesloub Fatiha Mesloub 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(10):3195-3208
For a coupled nonlinear singular system of thermoelasticity with one space dimension, we consider its initial boundary value problem on an interval. For one of the unknowns a classical condition is replaced by a nonlocal constraint of integral type. Because of the presence of a memory term in one of the equations and the presence of a weighted boundary integral condition, the solution requires a delicate set of techniques. We first solve a particular case of the given nonlinear problem by using a functional analysis approach. On the basis of the results obtained and an iteration method we establish the well-posedness of solutions in weighted Sobolev spaces. 相似文献
18.
Zhilei Liang 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(11):3507-3512
The present paper is concerned with the blow up rate of a solution to the following Cauchy problem
19.
In this paper, we discuss the critical exponents and non-extinction property for a nonlinear boundary value problem of a fast diffusive polytropic filtration equation. 相似文献
20.
Goro Akagi Kazumasa Suzuki 《Calculus of Variations and Partial Differential Equations》2008,31(4):457-471
The existence, uniqueness and regularity of viscosity solutions to the Cauchy–Dirichlet problem are proved for a degenerate
nonlinear parabolic equation of the form , where denotes the so-called infinity-Laplacian given by . To do so, a coercive regularization of the equation is introduced and barrier function arguments are also employed to verify
the equi-continuity of approximate solutions. Furthermore, the Cauchy problem is also studied by using the preceding results
on the Cauchy–Dirichlet problem.
Dedicated to the memory of our friend Kyoji Takaichi.
The research of the first author was partially supported by Waseda University Grant for Special Research Projects, #2004A-366. 相似文献