American Institute of Mathematical Sciences

Advanced
February  2009, 3(1): 17-41. doi: 10.3934/ipi.2009.3.17

A positivity principle for parabolic integro-differential equations and inverse problems with final overdetermination

Jaan Janno 1, and  Kairi Kasemets 2,

1. 

Institute of Cybernetics and Institute of Mathematics, Tallinn University of Technology, Akadeemia tee 21, Tallinn, 12618, Estonia
2. 

Institute of Mathematics, Tallinn University of Technology, Ehitajate tee 5, Tallinn, 12618, Estonia

Received  June 2008 Revised  January 2009 Published  February 2009

A positivity principle for parabolic integro-differential equations is proved. By means of this principle, uniqueness, existence and stability for an inverse source problem and two inverse coefficient problems are established.
Keywords: final overdetermination., inverse problem, parabolic integro-differential equation, extremum principle.
Mathematics Subject Classification: 35B50, 35R3.
Citation: Jaan Janno, Kairi Kasemets. A positivity principle for parabolic integro-differential equations and inverse problems with final overdetermination. Inverse Problems & Imaging, 2009, 3 (1) : 17-41. doi: 10.3934/ipi.2009.3.17
[1]

Kenichi Sakamoto, Masahiro Yamamoto. Inverse source problem with a final overdetermination for a fractional diffusion equation. Mathematical Control & Related Fields, 2011, 1 (4) : 509-518. doi: 10.3934/mcrf.2011.1.509
[2]

Walter Allegretto, John R. Cannon, Yanping Lin. A parabolic integro-differential equation arising from thermoelastic contact. Discrete & Continuous Dynamical Systems - A, 1997, 3 (2) : 217-234. doi: 10.3934/dcds.1997.3.217
[3]

Tianling Jin, Jingang Xiong. Schauder estimates for solutions of linear parabolic integro-differential equations. Discrete & Continuous Dynamical Systems - A, 2015, 35 (12) : 5977-5998. doi: 10.3934/dcds.2015.35.5977
[4]

Narcisa Apreutesei, Nikolai Bessonov, Vitaly Volpert, Vitali Vougalter. Spatial structures and generalized travelling waves for an integro-differential equation. Discrete & Continuous Dynamical Systems - B, 2010, 13 (3) : 537-557. doi: 10.3934/dcdsb.2010.13.537
[5]

Shihchung Chiang. Numerical optimal unbounded control with a singular integro-differential equation as a constraint. Conference Publications, 2013, 2013 (special) : 129-137. doi: 10.3934/proc.2013.2013.129
[6]

Frederic Abergel, Remi Tachet. A nonlinear partial integro-differential equation from mathematical finance. Discrete & Continuous Dynamical Systems - A, 2010, 27 (3) : 907-917. doi: 10.3934/dcds.2010.27.907
[7]

Samir K. Bhowmik, Dugald B. Duncan, Michael Grinfeld, Gabriel J. Lord. Finite to infinite steady state solutions, bifurcations of an integro-differential equation. Discrete & Continuous Dynamical Systems - B, 2011, 16 (1) : 57-71. doi: 10.3934/dcdsb.2011.16.57
[8]

Michel Chipot, Senoussi Guesmia. On a class of integro-differential problems. Communications on Pure & Applied Analysis, 2010, 9 (5) : 1249-1262. doi: 10.3934/cpaa.2010.9.1249
[9]

Cyril Imbert, Sylvia Serfaty. Repeated games for non-linear parabolic integro-differential equations and integral curvature flows. Discrete & Continuous Dynamical Systems - A, 2011, 29 (4) : 1517-1552. doi: 10.3934/dcds.2011.29.1517
[10]

Luis Silvestre. Hölder continuity for integro-differential parabolic equations with polynomial growth respect to the gradient. Discrete & Continuous Dynamical Systems - A, 2010, 28 (3) : 1069-1081. doi: 10.3934/dcds.2010.28.1069
[11]

Nestor Guillen, Russell W. Schwab. Neumann homogenization via integro-differential operators. Discrete & Continuous Dynamical Systems - A, 2016, 36 (7) : 3677-3703. doi: 10.3934/dcds.2016.36.3677
[12]

Olivier Bonnefon, Jérôme Coville, Jimmy Garnier, Lionel Roques. Inside dynamics of solutions of integro-differential equations. Discrete & Continuous Dynamical Systems - B, 2014, 19 (10) : 3057-3085. doi: 10.3934/dcdsb.2014.19.3057
[13]

Paola Loreti, Daniela Sforza. Observability of $N$-dimensional integro-differential systems. Discrete & Continuous Dynamical Systems - S, 2016, 9 (3) : 745-757. doi: 10.3934/dcdss.2016026
[14]

Dariusz Idczak, Stanisław Walczak. Necessary optimality conditions for an integro-differential Bolza problem via Dubovitskii-Milyutin method. Discrete & Continuous Dynamical Systems - B, 2019, 24 (5) : 2281-2292. doi: 10.3934/dcdsb.2019095
[15]

Giuseppe Maria Coclite, Mario Michele Coclite. Positive solutions of an integro-differential equation in all space with singular nonlinear term. Discrete & Continuous Dynamical Systems - A, 2008, 22 (4) : 885-907. doi: 10.3934/dcds.2008.22.885
[16]

Jean-Michel Roquejoffre, Juan-Luis Vázquez. Ignition and propagation in an integro-differential model for spherical flames. Discrete & Continuous Dynamical Systems - B, 2002, 2 (3) : 379-387. doi: 10.3934/dcdsb.2002.2.379
[17]

Tomás Caraballo, P.E. Kloeden. Non-autonomous attractors for integro-differential evolution equations. Discrete & Continuous Dynamical Systems - S, 2009, 2 (1) : 17-36. doi: 10.3934/dcdss.2009.2.17
[18]

Liang Zhang, Bingtuan Li. Traveling wave solutions in an integro-differential competition model. Discrete & Continuous Dynamical Systems - B, 2012, 17 (1) : 417-428. doi: 10.3934/dcdsb.2012.17.417
[19]

Yubo Chen, Wan Zhuang. The extreme solutions of PBVP for integro-differential equations with caratheodory functions. Conference Publications, 1998, 1998 (Special) : 160-166. doi: 10.3934/proc.1998.1998.160
[20]

Narcisa Apreutesei, Arnaud Ducrot, Vitaly Volpert. Travelling waves for integro-differential equations in population dynamics. Discrete & Continuous Dynamical Systems - B, 2009, 11 (3) : 541-561. doi: 10.3934/dcdsb.2009.11.541

2018 Impact Factor: 1.469

Tools

Metrics

  • PDF downloads (64)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences