On Non-existence of Global Weak-predictable-random-field Solutions to a Class of SHEs
On Non-existence of Global Weak-predictable-random-field Solutions to a Class of SHEs
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关于一类 SHE 的全局弱可预测随机场解的不存在性
DOI：
10.9734/arjom/2017/33317
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
L. Omenyi
中科院分区：
文献类型：
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作者：
Ejighikeme Mcsylvester Omaba;E. Nwaeze;L. Omenyi
在大多数关于SPDEs的结果中，乘法非线性项通常被假定为全局Lipschitz。本文证明了当非线性项增长速度大于线性项增长速度时，解不存在。在某些非线性条件下，解全局不存在。给出了解的存在唯一性的一些精确条件，并证明了解在一定时间间隔内最多以精确指数速率随时间增长；如果解满足一些非线性条件那么它们在有限时间t停止存在。我们的结果还比较了补偿和非补偿泊松噪声方程的全局解的不存在性
The multiplicative non-linearity term is usually assumed to be globally Lipschitz in most results on SPDEs. This work proves that the solutions fail to exist if the non-linearity term grows faster than linear growth. The global non-existence of the solution occurs for some non-linear conditions on $\sigma$ . Some precise conditions for existence and uniqueness of the solutions were stated and we have established that the solutions grow in time at most a precise exponential rate at some time interval; and if the solutions satisfy some non-linear conditions then they cease to exist at some finite time t . Our result also compares the non-existence of global solutions for both the compensated and non-compensated Poisson noise equations