Local existence of solutions to the initial-value problem for one-dimensional strain-limiting viscoelasticity

Name: Local existence of solutions to the initial-value problem for one-dimensional strain-limiting viscoelasticity
Author: Erbay, Hüsnü Ata, Erkip, A., Şengül, Y.

İsim	Local existence of solutions to the initial-value problem for one-dimensional strain-limiting viscoelasticity
Yazar	Erbay, Hüsnü Ata, Erkip, A., Şengül, Y.
Basım Tarihi:	2020-11-15
Basım Yeri	- Elsevier
Konu	Viscoelasticity, Strain-limiting theory, Initial-value problem, Local existence
Tür	Süreli Yayın
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	0022-0396
Kayıt Numarası	fe238ab2-62d6-49e8-a560-b742ff67e26b
Lokasyon	Natural and Mathematical Sciences
Tarih	2020-11-15
Notlar	TÜBİTAK
Örnek Metin	In this work we prove local existence of strong solutions to the initial-value problem arising in one-dimensional strain-limiting viscoelasticity, which is based on a nonlinear constitutive relation between the linearized strain, the rate of change of the linearized strain and the stress. The model is a generalization of the nonlinear Kelvin-Voigt viscoelastic solid under the assumption that the strain and the strain rate are small. We define an initial-value problem for the stress variable and then, under the assumption that the nonlinear constitutive function is strictly increasing, we convert the problem to a new form for the sum of the strain and the strain rate. Using the theory of variable coefficient heat equation together with a fixed point argument we prove local existence of solutions. Finally, for several constitutive functions widely used in the literature we show that the assumption on which the proof of existence is based is not violated.
DOI	10.1016/j.jde.2020.06.052
Cilt	269

Kaynağa git Özyeğin Üniversitesi

Aramaya Dön

Özyeğin Üniversitesi

Kaynağa git

Local existence of solutions to the initial-value problem for one-dimensional strain-limiting viscoelasticity

Yazar Erbay, Hüsnü Ata, Erkip, A., Şengül, Y.

Basım Tarihi 2020-11-15

Basım Yeri - Elsevier

Konu Viscoelasticity, Strain-limiting theory, Initial-value problem, Local existence

Tür Süreli Yayın

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası 0022-0396

Kayıt Numarası fe238ab2-62d6-49e8-a560-b742ff67e26b

Lokasyon Natural and Mathematical Sciences

Tarih 2020-11-15

Notlar TÜBİTAK

Örnek Metin In this work we prove local existence of strong solutions to the initial-value problem arising in one-dimensional strain-limiting viscoelasticity, which is based on a nonlinear constitutive relation between the linearized strain, the rate of change of the linearized strain and the stress. The model is a generalization of the nonlinear Kelvin-Voigt viscoelastic solid under the assumption that the strain and the strain rate are small. We define an initial-value problem for the stress variable and then, under the assumption that the nonlinear constitutive function is strictly increasing, we convert the problem to a new form for the sum of the strain and the strain rate. Using the theory of variable coefficient heat equation together with a fixed point argument we prove local existence of solutions. Finally, for several constitutive functions widely used in the literature we show that the assumption on which the proof of existence is based is not violated.

DOI 10.1016/j.jde.2020.06.052

Cilt 269