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The multiplicative non-linearity term is usually assumed to be globallyLipschitz in most results on SPDEs. This work proves that the solutions fail toexist if the non-linearity term grows faster than linear growth. The globalnon-existence of the solution occurs for some non-linear conditions on $\sigma$. Some precise conditions for existence and uniqueness of the solutions werestated and we have established that the solutions grow in time at most aprecise exponential rate at some time interval; and if the solutions satisfysome non-linear conditions then they cease to exist at some finite time t . Ourresult also compares the non-existence of global solutions for both thecompensated and non-compensated Poisson noise equations

On Non-existence of Global Weak-predictable-random-field Solutions to a Class of SHEs