共查询到20条相似文献,搜索用时 0 毫秒
1.
对如下形式的非线性抛物方程ut=up(uu)-uq,inQ∞=Ω×(0,∞)当p<1时,讨论了其解的大时间渐近性. 相似文献
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研究了具有依赖于时间的系数的非线性抛物方程解的爆破现象.对已知数据项进行一定的假设并设置一些辅助函数,应用微分不等式技术,得到了方程的解发生爆破的条件.当爆破发生时,分别推导了方程在二维区域和三维区域上解的爆破时间的下界. 相似文献
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研究一类在非均匀介质中带可变系数和吸收项的非线性退化抛物方程Cauchy问题解的局部性质和渐近行为,得到了解有局部性的条件.同时,证明了解的渐近性质,发现了有限时刻的熄灭现象.这些结果改进和推广了相关问题的最新成果. 相似文献
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We reduce the construction of a weak solution of the Cauchy problem for a quasilinear parabolic equation to the construction
of a solution to a stochastic problem. Namely, we construct a diffusion process that allows us to obtain a probabilistic representation
of a weak (in distributional sense) solution to the Cauchy problem for a nonlinear PDE.
相似文献
7.
Existence and Asymptotic Behavior of Radially Symmetric Solutions to a Semilinear Hyperbolic System in Odd Space Dimensions 下载免费PDF全文
This paper is concerned with a class of semilinear hyperbolic systems in odd space dimensions. Our main aim is to prove the existence of a small amplitude solution which is asymptotic to the free solution as t→-∞in the energy norm, and to show it has a free profile as t→ ∞. Our approach is based on the work of [11]. Namely we use a weighted L∞norm to get suitable a priori estimates. This can be done by restricting our attention to radially symmetric solutions. Corresponding initial value problem is also considered in an analogous framework. Besides, we give an extended result of [14] for three space dimensional case in Section 5, which is prepared independently of the other parts of the paper. 相似文献
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We consider a three-component reaction-diffusion system with a reaction rate parameter, and investigate its singular limit as the reaction rate tends to infinity. The limit problem is given by a free boundary problem which possesses three regions separated by the free boundaries. One component vanishes and the other two components remain positive in each region. Therefore, the dynamics is governed by a system of two equations. 相似文献
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Hui Feng & Longjun Shen 《计算数学(英文版)》1998,16(5):395-402
In this paper we prove that the solution of implicit difference scheme for a semilinear parabolic equation converges to the solution of difference scheme for the corresponding nonlinear stationary problem as $t\rightarrow\infty$. For the discrete solution of nonlinear parabolic problem, we get its long time asymptotic behavior which is similar to that of the continuous solution. For simplicity, we consider one-dimensional problem. 相似文献
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Takayoshi Ogawa 《Journal of Differential Equations》2011,251(11):3090-3113
We consider the Cauchy problem of the semilinear damped wave system:
11.
In this paper, we give some regularity results of solutions to nonlinear parabolic equations with a lower-order term and inregular data. 相似文献
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ABSTRACT The Cauchy problem for two dimensional difference wave operators is considered with potentials and initial data supported in a bounded region. The large time asymptotic behavior of solutions is obtained. In contrast to the continuous case (when the problem in the Euclidian space is considered, not on the lattice) the resolvent of the corresponding stationary problem has singularities on the continuous spectrum, and they contribute to the asymptotics. 相似文献
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Zhijun ZHANG 《数学年刊B辑(英文版)》2020,41(4):601-614
This paper is concerned with strictly k-convex large solutions to Hessian equations Sk(D2u(x)) = b(x)f(u(x)), x ∈ ?, where ? is a strictly(k-1)-convex and bounded smooth domain in Rn, b ∈ C∞(?) is positive in ?, but may be vanishing on the boundary.Under a new structure condition on f at infinity, the author studies the refined boundary behavior of such solutions. The results are obtained in a more general setting than those in [Huang, Y., Boundary asymptotical b... 相似文献
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研究了一类具有非线性边界条件的拟线性方程组解的整体存在性和爆破.通过构造不同类型的上、下解并利用M-矩阵的基本性质,给出了非负解整体存在性的充要条件.借助这些新结果,给出了Fuiita型临界曲线,把最近的结果推广到了更一般的方程. 相似文献
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In [7] we show the global existence and uniqueness of a solution of carbon dioxide transport model in concrete carbonation process. This model is governed by a parabolic-type equation which has a non-local term depending on the unknown function itself. In this paper, we show the large time behavior of that solution. 相似文献
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Frank Jochmann 《Journal of Differential Equations》2004,203(2):232-254
In this paper, Maxwell's equations involving generally nonlinear polarization and field-dependent currents are studied. The main objective is the asymptotic behavior of the solution for t→∞ if no damping term occurs in the equation governing the polarization field. 相似文献
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研究了可压缩Navier-Stokes方程组
球对称弱解的大时间行为. 假设压强
$p(\varrho)=\varrho^\gamma$, 绝热指数$\gamma>1$, 外力是球对称的. 证明了假如外力满足一定的正则性及某种结构性条件, 则当时间
趋于无穷大时, 密度将趋于其对应的静止问题的唯一解. 相似文献
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This paper concerns large time behavior of a regular weak solution for non-Newtonian flow equations. It is shown that the decay of the solution is of exponential type when the force term is equal to zero and the domain is bounded. Moreover, the ratio of the enstrophy over the energy has a limit as time tends to infinity, which is an eigenvalue of the Stokes operator. 相似文献