American Institute of Mathematical Sciences

Advanced
2005, 2005(Special): 386-396. doi: 10.3934/proc.2005.2005.386

A class of integrodifferential equations and applications

Min He 1,

1. 

Department of Mathematical Sciences, Kent State University-Trumbull Campus, Warren, Ohio 44483, United States

Received  September 2004 Revised  April 2005 Published  September 2005

This work considers an abstract integrodifferential equation in Banach space: \be & &u'(t)=A(\ep)\left[u(t)+\int_0^t F(t-s)u(s)\,ds\right]+Ku(t)+f(t), \,\,t\ge0, \nonumber\\ & &u(0)=u_0, \nonumber \ee where $A(\ep)$ is a closed, linear, and non-densely defined operator, $\ep$ is a multi-parameter, and $K$ and $F(t)$ are bounded operators. The purpose of this work is to study effect of the parameter on the solution of the equation. The approach used is based on the integrated semigroup theory. Two methods are employed to determine the continuity in parameter $\ep$ of integrated semigroup, which is generated by $A(\ep)$. The main theorems on the integrated semigroup can be effectively used to obtain the similar results for the solution of the equation. The applications of these results to some equations of viscoelasticity are discussed.
Keywords: Integrated semigroup, Continuity ., Parameter.
Mathematics Subject Classification: Primary: 47D62, 45K05; Secondary: 35L2.
Citation: Min He. A class of integrodifferential equations and applications. Conference Publications, 2005, 2005 (Special) : 386-396. doi: 10.3934/proc.2005.2005.386
[1]

Min He. On continuity in parameters of integrated semigroups. Conference Publications, 2003, 2003 (Special) : 403-412. doi: 10.3934/proc.2003.2003.403
[2]

Viorel Nitica, Andrei Török. On a semigroup problem. Discrete & Continuous Dynamical Systems - S, 2019, 12 (8) : 2365-2377. doi: 10.3934/dcdss.2019148
[3]

Ethan Akin. On chain continuity. Discrete & Continuous Dynamical Systems, 1996, 2 (1) : 111-120. doi: 10.3934/dcds.1996.2.111
[4]

J. W. Neuberger. How to distinguish a local semigroup from a global semigroup. Discrete & Continuous Dynamical Systems, 2013, 33 (11&12) : 5293-5303. doi: 10.3934/dcds.2013.33.5293
[5]

Andrzej Biś. Entropies of a semigroup of maps. Discrete & Continuous Dynamical Systems, 2004, 11 (2&3) : 639-648. doi: 10.3934/dcds.2004.11.639
[6]

Michael Blank. Recurrence for measurable semigroup actions. Discrete & Continuous Dynamical Systems, 2021, 41 (4) : 1649-1665. doi: 10.3934/dcds.2020335
[7]

Carlos Cabrera, Peter Makienko, Peter Plaumann. Semigroup representations in holomorphic dynamics. Discrete & Continuous Dynamical Systems, 2013, 33 (4) : 1333-1349. doi: 10.3934/dcds.2013.33.1333
[8]

Jana Kopfová. Nonlinear semigroup methods in problems with hysteresis. Conference Publications, 2007, 2007 (Special) : 580-589. doi: 10.3934/proc.2007.2007.580
[9]

Renato Iturriaga, Héctor Sánchez Morgado. The Lax-Oleinik semigroup on graphs. Networks & Heterogeneous Media, 2017, 12 (4) : 643-662. doi: 10.3934/nhm.2017026
[10]

Miriam Kiessling, Sascha Kurz, Jörg Rambau. The integrated size and price optimization problem. Numerical Algebra, Control & Optimization, 2012, 2 (4) : 669-693. doi: 10.3934/naco.2012.2.669
[11]

Maria Colombo, Gianluca Crippa, Stefano Spirito. Logarithmic estimates for continuity equations. Networks & Heterogeneous Media, 2016, 11 (2) : 301-311. doi: 10.3934/nhm.2016.11.301
[12]

Dongkui Ma, Min Wu. Topological pressure and topological entropy of a semigroup of maps. Discrete & Continuous Dynamical Systems, 2011, 31 (2) : 545-556. doi: 10.3934/dcds.2011.31.545
[13]

Bin Chen, Xiongping Dai. On uniformly recurrent motions of topological semigroup actions. Discrete & Continuous Dynamical Systems, 2016, 36 (6) : 2931-2944. doi: 10.3934/dcds.2016.36.2931
[14]

Luisa Arlotti. Explicit transport semigroup associated to abstract boundary conditions. Conference Publications, 2011, 2011 (Special) : 102-111. doi: 10.3934/proc.2011.2011.102
[15]

Stephen Thompson, Thomas I. Seidman. Approximation of a semigroup model of anomalous diffusion in a bounded set. Evolution Equations & Control Theory, 2013, 2 (1) : 173-192. doi: 10.3934/eect.2013.2.173
[16]

Armand Bernou. A semigroup approach to the convergence rate of a collisionless gas. Kinetic & Related Models, 2020, 13 (6) : 1071-1106. doi: 10.3934/krm.2020038
[17]

Sanyi Tang, Lansun Chen. Modelling and analysis of integrated pest management strategy. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 759-768. doi: 10.3934/dcdsb.2004.4.759
[18]

Yujun Ju, Dongkui Ma, Yupan Wang. Topological entropy of free semigroup actions for noncompact sets. Discrete & Continuous Dynamical Systems, 2019, 39 (2) : 995-1017. doi: 10.3934/dcds.2019041
[19]

Klara Stokes, Maria Bras-Amorós. Associating a numerical semigroup to the triangle-free configurations. Advances in Mathematics of Communications, 2011, 5 (2) : 351-371. doi: 10.3934/amc.2011.5.351
[20]

Gérard Maze, Chris Monico, Joachim Rosenthal. Public key cryptography based on semigroup actions. Advances in Mathematics of Communications, 2007, 1 (4) : 489-507. doi: 10.3934/amc.2007.1.489

 Impact Factor: 

Tools

Metrics

  • PDF downloads (37)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences