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Explosive solutions of a stochastic non-local reaction–diffusion equation arising in shear band formation
Kavallaris, Nikos I.
Kavallaris, Nikos I.
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2015-07-07
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Abstract
In this paper, we consider a non-local stochastic parabolic equation which actually serves as a mathematical model describing the adiabatic shear-banding formation phenomena in strained metals. We first present the derivation of the mathematical model. Then we investigate under which circumstances a finite-time explosion for this non-local SPDE, corresponding to shear-banding formation, occurs. For that purpose some results related to the maximum principle for this non-local SPDE are derived and afterwards the Kaplan's eigenfunction method is employed.
Citation
Kavallaris, N. I. (2015). "Explosive solutions of a stochastic non-local reaction–diffusion equation arising in shear band formation." Mathematical Methods in the Applied Sciences 38(16): 3564-3574. DOI: 10.1002/mma.3514
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Wiley
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Mathematical Methods in the Applied Sciences
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Article
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en
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This is the peer reviewed version of the following article: Kavallaris, N. I. (2015). Explosive solutions of a stochastic non-local reaction–diffusion equation arising in shear band formation. Mathematical Methods in the Applied Sciences 38(16): 3564-3574, which has been published in final form at DOI: 10.1002/mma.3514. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
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Non-local, Stochastic Partial Differential Equations, Maximum principle, Blow-up, Shear band formation
ISSN
0170-4214
EISSN
1099-1476