American Institute of Mathematical Sciences

Advanced
May  2010, 13(3): 517-535. doi: 10.3934/dcdsb.2010.13.517

Global solutions for an age-dependent model of nucleation, growth and ageing with hysteresis

Youssef Amal 1, and  Martin Campos Pinto 2,

1. 

Université de Strasbourg et CNRS, C.G.S., 1 rue Blessig, 67084 Strasbourg Cedex, France
2. 

Université de Strasbourg et CNRS, I.R.M.A., 7 rue René Descartes, 67084 Strasbourg Cedex, France

Received  September 2008 Revised  May 2009 Published  February 2010

In this article we establish the global well-posedness of a recent model proposed by Noguera, Fritz, Clément and Baronnet for simultaneously describing the process of nucleation, growth and ageing of particles in thermodynamically closed and initially supersaturated systems. This model, which applies to precipitation in solution, vapor condensation and crystallization from a simple melt, can be seen as a highly nonlinear age-dependent population problem involving a delayed birth process and a hysteresis damage operator.
Keywords: Age-dependent growth model, existence of global solutions., integral equations, hysteresis.
Mathematics Subject Classification: Primary: 35A05, 45G; Secondary: 47J40, 92D2.
Citation: Youssef Amal, Martin Campos Pinto. Global solutions for an age-dependent model of nucleation, growth and ageing with hysteresis. Discrete and Continuous Dynamical Systems - B, 2010, 13 (3) : 517-535. doi: 10.3934/dcdsb.2010.13.517
[1]

Shanjing Ren. Global stability in a tuberculosis model of imperfect treatment with age-dependent latency and relapse. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 1337-1360. doi: 10.3934/mbe.2017069
[2]

Antoni Leon Dawidowicz, Anna Poskrobko. Stability problem for the age-dependent predator-prey model. Evolution Equations and Control Theory, 2018, 7 (1) : 79-93. doi: 10.3934/eect.2018005
[3]

Christoph Walker. Age-dependent equations with non-linear diffusion. Discrete and Continuous Dynamical Systems, 2010, 26 (2) : 691-712. doi: 10.3934/dcds.2010.26.691
[4]

Bedr'Eddine Ainseba. Age-dependent population dynamics diffusive systems. Discrete and Continuous Dynamical Systems - B, 2004, 4 (4) : 1233-1247. doi: 10.3934/dcdsb.2004.4.1233
[5]

Andrey V. Melnik, Andrei Korobeinikov. Lyapunov functions and global stability for SIR and SEIR models with age-dependent susceptibility. Mathematical Biosciences & Engineering, 2013, 10 (2) : 369-378. doi: 10.3934/mbe.2013.10.369
[6]

Jinliang Wang, Xianning Liu, Toshikazu Kuniya, Jingmei Pang. Global stability for multi-group SIR and SEIR epidemic models with age-dependent susceptibility. Discrete and Continuous Dynamical Systems - B, 2017, 22 (7) : 2795-2812. doi: 10.3934/dcdsb.2017151
[7]

Peng Yang, Yuanshi Wang. On oscillations to a 2D age-dependent predation equations characterizing Beddington-DeAngelis type schemes. Discrete and Continuous Dynamical Systems - B, 2022, 27 (7) : 3845-3895. doi: 10.3934/dcdsb.2021209
[8]

Gabriella Di Blasio. An ultraparabolic problem arising from age-dependent population diffusion. Discrete and Continuous Dynamical Systems, 2009, 25 (3) : 843-858. doi: 10.3934/dcds.2009.25.843
[9]

Sainan Wu, Junping Shi, Boying Wu. Global existence of solutions to an attraction-repulsion chemotaxis model with growth. Communications on Pure and Applied Analysis, 2017, 16 (3) : 1037-1058. doi: 10.3934/cpaa.2017050
[10]

Patricia J.Y. Wong. Existence of solutions to singular integral equations. Conference Publications, 2009, 2009 (Special) : 818-827. doi: 10.3934/proc.2009.2009.818
[11]

Zijuan Wen, Meng Fan, Asim M. Asiri, Ebraheem O. Alzahrani, Mohamed M. El-Dessoky, Yang Kuang. Global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with application to a glioblastoma growth model. Mathematical Biosciences & Engineering, 2017, 14 (2) : 407-420. doi: 10.3934/mbe.2017025
[12]

Yang Liu. Global existence and exponential decay of strong solutions to the cauchy problem of 3D density-dependent Navier-Stokes equations with vacuum. Discrete and Continuous Dynamical Systems - B, 2021, 26 (3) : 1291-1303. doi: 10.3934/dcdsb.2020163
[13]

Akisato Kubo, Hiroki Hoshino, Katsutaka Kimura. Global existence and asymptotic behaviour of solutions for nonlinear evolution equations related to a tumour invasion model. Conference Publications, 2015, 2015 (special) : 733-744. doi: 10.3934/proc.2015.0733
[14]

Qian Zhao, Bin Liu. Global generalized solutions to the forager-exploiter model with logistic growth. Discrete and Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021273
[15]

Nguyen Lam, Guozhen Lu. Existence of nontrivial solutions to Polyharmonic equations with subcritical and critical exponential growth. Discrete and Continuous Dynamical Systems, 2012, 32 (6) : 2187-2205. doi: 10.3934/dcds.2012.32.2187
[16]

Jianxin Yang, Zhipeng Qiu, Xue-Zhi Li. Global stability of an age-structured cholera model. Mathematical Biosciences & Engineering, 2014, 11 (3) : 641-665. doi: 10.3934/mbe.2014.11.641
[17]

Yuming Chen, Junyuan Yang, Fengqin Zhang. The global stability of an SIRS model with infection age. Mathematical Biosciences & Engineering, 2014, 11 (3) : 449-469. doi: 10.3934/mbe.2014.11.449
[18]

Mohammed Nor Frioui, Tarik Mohammed Touaoula, Bedreddine Ainseba. Global dynamics of an age-structured model with relapse. Discrete and Continuous Dynamical Systems - B, 2020, 25 (6) : 2245-2270. doi: 10.3934/dcdsb.2019226
[19]

G. C. Yang, K. Q. Lan. Systems of singular integral equations and applications to existence of reversed flow solutions of Falkner-Skan equations. Communications on Pure and Applied Analysis, 2013, 12 (6) : 2465-2495. doi: 10.3934/cpaa.2013.12.2465
[20]

Fatima Zohra Hathout, Tarik Mohammed Touaoula, Salih Djilali. Mathematical analysis of a triple age dependent epidemiological model with including a protection strategy. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022048

2020 Impact Factor: 1.327

Tools

Metrics

  • PDF downloads (73)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy