一类SHE整体弱可料随机场解的不存在性
On Non-existence of Global Weak-predictable-random-field Solutions to a Class of SHEs
摘要：
在SPDE的大多数结果中，乘性非线性项通常被假设为全局Lipschitz。证明了当非线性项的增长速度大于线性项的增长速度时，解不存在。对于$σ$上的某些非线性条件，存在解的全局不存在性.给出了解的存在唯一性的精确条件，并建立了解在某个时间间隔内至多以精确的指数速率增长;如果解满足某些非线性条件，则在某个有限时刻t不再存在.我们的结果还比较了补偿和非补偿Poisson噪声方程整体解的不存在性
英文摘要：
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 $σ$ . 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
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