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Local existence of a solution to a free boundary problem describing migration into rubber with a breaking effect
Nagasaki University, JPN.
Japan Women's University, JPN.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).ORCID iD: 0000-0002-1160-0007
2023 (English)In: Networks and Heterogeneous Media, ISSN 1556-1801, E-ISSN 1556-181X, Vol. 18, no 1, p. 80-108Article in journal (Refereed) Published
Abstract [en]

We consider a one-dimensional free boundary problem describing the migration of diffusants into rubber. In our setting, the free boundary represents the position of the front delimitating the diffusant region. The growth rate of this region is described by an ordinary differential equation that includes the effect of breaking the growth of the diffusant region. In this specific context, the breaking mechanism is should be perceived as a non-dissipative way of describing eventual hyperelastic response to a too fast diffusion penetration. In recent works, we considered a similar class of free boundary problems modeling diffusants penetration in rubbers, but without attempting to deal with the possibility of breaking or accelerating the occurring free boundaries. For simplified settings, we were able to show the global existence and uniqueness as well as the large time behavior of the corresponding solutions to our formulations. Since here the breaking effect is contained in the free boundary condition, our previous results are not anymore applicable. The main mathematical obstacle in ensuring the existence of a solution is the non-monotonic structure of the free boundary. In this paper, we establish the existence and uniqueness of a weak solution to the free boundary problem with breaking effect and give explicitly the maximum value that the free boundary can reach. 

Place, publisher, year, edition, pages
American Institute of Mathematical Sciences, 2023. Vol. 18, no 1, p. 80-108
Keywords [en]
migration into rubber, free boundary problem, nonlinear initial-boundary value problem for nonlinear parabolic equations, existence of solutions, Flux boundary condition
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-92496DOI: 10.3934/nhm.2023004ISI: 000922644200004Scopus ID: 2-s2.0-85140482035OAI: oai:DiVA.org:kau-92496DiVA, id: diva2:1711286
Available from: 2022-11-16 Created: 2022-11-16 Last updated: 2023-02-25Bibliographically approved

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Muntean, Adrian

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