Explosive solutions of a stochastic non-local reaction–diffusion equation arising in shear band formation

Hdl Handle:
http://hdl.handle.net/10034/556204
Title:
Explosive solutions of a stochastic non-local reaction–diffusion equation arising in shear band formation
Authors:
Kavallaris, Nikos I.
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.
Affiliation:
University of Chester
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
Publisher:
Wiley
Journal:
Mathematical Methods in the Applied Sciences
Publication Date:
3-Jun-2015
URI:
http://hdl.handle.net/10034/556204
Additional Links:
http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1476
Type:
Article
Language:
en
Description:
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.
Series/Report no.:
Non-local, Stochastic Partial Differential Equations, Maximum principle, Blow-up, Shear band formation
ISSN:
0170-4214
EISSN:
1099-1476
Appears in Collections:
Mathematics

Full metadata record

DC FieldValue Language
dc.contributor.authorKavallaris, Nikos I.en
dc.date.accessioned2015-06-03T13:46:41Zen
dc.date.available2015-06-03T13:46:41Zen
dc.date.issued2015-06-03en
dc.identifier.citationKavallaris, 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.3514en
dc.identifier.issn0170-4214en
dc.identifier.urihttp://hdl.handle.net/10034/556204en
dc.descriptionThis 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.en
dc.description.abstractIn 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.en
dc.language.isoenen
dc.publisherWileyen
dc.relation.ispartofseriesNon-local, Stochastic Partial Differential Equations, Maximum principle, Blow-up, Shear band formationen
dc.relation.urlhttp://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1476en
dc.rightsAn error occurred on the license name.*
dc.rights.uriAn error occurred getting the license - uri.*
dc.titleExplosive solutions of a stochastic non-local reaction–diffusion equation arising in shear band formationen
dc.typeArticleen
dc.identifier.eissn1099-1476en
dc.contributor.departmentUniversity of Chesteren
dc.identifier.journalMathematical Methods in the Applied Sciencesen
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