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

Ejighikeme McSylvester Omaba; Emmanuel Nwaeze; Louis Okechukwu Omenyi

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arXiv · 1706.02403

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

Ejighikeme McSylvester Omaba·Emmanuel Nwaeze·Louis Okechukwu Omenyi

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Abstract

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

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Ejighikeme McSylvester Omaba, Emmanuel Nwaeze, Louis Okechukwu Omenyi. 2017-06-07. On Non-existence of Global Weak-predictable-random-field Solutions to a Class of SHEs. https://arxiv.org/abs/1706.02403

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