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

E. M. Omaba; E. Nwaeze; L. O. Omenyi

doi:10.9734/ARJOM/2017/33317

Research Article Open access CC BY 4.0

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

E. M. Omaba, E. Nwaeze, L. O. Omenyi

Asian Research Journal of Mathematics · pp. 1–14 · Published 12 May 2017

10.9734/ARJOM/2017/33317

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 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.

Random field solution weak predictable solution global solution Non-existence

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E. M. Omaba, E. Nwaeze, L. O. Omenyi (2017). On Non-existence of Global Weak-predictable-random-field Solutions to a Class of SHEs. Asian Research Journal of Mathematics , 1–14. https://doi.org/10.9734/ARJOM/2017/33317

Affiliations

E. M. Omaba — Department of Mathematics, Computer Science, Statistics and Informatics, Faculty of Science, Federal University Ndufu-Alike, Ikwo, P.M.B. 1010, Abakaliki, Ebonyi State, Nigeria.
E. Nwaeze — Department of Mathematics, Computer Science, Statistics and Informatics, Faculty of Science, Federal University Ndufu-Alike, Ikwo, P.M.B. 1010, Abakaliki, Ebonyi State, Nigeria.
L. O. Omenyi — Department of Mathematics, Computer Science, Statistics and Informatics, Faculty of Science, Federal University Ndufu-Alike, Ikwo, P.M.B. 1010, Abakaliki, Ebonyi State, Nigeria.

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