Continuous dependence on the coefficients and global existence for stochastic reaction diffusion equations
Continuous dependence on the coefficients and global existence for stochastic reaction diffusion equations
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随机反应扩散方程对系数和全局存在性的连续依赖性
DOI：
10.1016/j.jde.2012.04.013
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
J. Neerven
中科院分区：
文献类型：
--
作者：
M. Kunze;J. Neerven
我们证明了巴纳赫空间 B 上半线性随机演化方程的解 Xn 的收敛性，由希尔伯特空间 H 中的圆柱布朗运动驱动，假设算子 An 收敛到 A，局部 Lipschitz 函数 Fn 和 Gn 在适当的意义上收敛到局部 Lipschitz 函数 F 和 G。此外，我们根据近似解 Xn 的寿命获得了极限问题解 X 的寿命估计。我们应用结果来证明具有乘性噪声和满足适当耗散条件的多项式有界反应项的反应扩散方程的全局存在性。控制方程线性部分的算子可以是任意一致椭圆二阶椭圆算子。
We prove convergence of the solutions Xnof semilinear stochastic evolution equations on a Banach space B, driven by a cylindrical Brownian motion in a Hilbert space H, assuming that the operators Anconverge to A and the locally Lipschitz functions Fnand Gnconverge to the locally Lipschitz functions F and G in an appropriate sense. Moreover, we obtain estimates for the lifetime of the solution X of the limiting problem in terms of the lifetimes of the approximating solutions Xn. We apply the results to prove global existence for reaction diffusion equations with multiplicative noise and a polynomially bounded reaction term satisfying suitable dissipativity conditions. The operator governing the linear part of the equation can be an arbitrary uniformly elliptic second-order elliptic operator.