Evolution Equations and Control Theory (EECT)

A strongly ill-posed integrodifferential singular parabolic problem in the unit cube of $\mathbb{R}^n$
Pages: 499 - 524, Issue 3, September 2014

doi:10.3934/eect.2014.3.499      Abstract        References        Full text (456.0K)           Related Articles

Alfredo Lorenzi - Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, Via Saldini 50, 20133, Milano, Italy (email)
Luca Lorenzi - Dipartimento di Matematica, Università degli Studi di Parma, Viale Parco Area delle Scienze 53/A, I-43124 Parma, Italy (email)

1 D. Bainov and P. Simeonov, Integral Inequalities and Applications, Translated by R. A. M. Hoksbergen and V. Covachev [V. Khr. Kovachev], Mathematics and its Applications (East European Series), 57, Kluwer Academic Publishers Group, Dordrecht, 1992.       
2 P. Cannarsa, J. Tort and M. Yamamoto, Determination of source terms in a degenerate parabolic equation, Inverse Problems, 26 (2010), 105003, 20 pp.       
3 M. Choulli, Une Introduction aux Problèms Inverses Elliptiques et Paraboliques, Mathematiques and Applications, 65, Springer-Verlag, Berlin Heidelberg, 2009.       
4 P. Lax, Functional Analysis, Wiley-Interscience, 2002.       
5 A. Lorenzi, Two strongly ill-posed problems, AIP Conference Proceedings, Melville, New York, 1329 (2011), 150-169.       
6 A. Lorenzi, Recovering a constant in a strongly ill-posed parabolic problem, J. Abstr. Differ. Equ. Appl., 2 (2012), 72-92.       
7 A. Lorenzi, Linear integro-differential Schrödinger and plate problems without initial conditions, Appl. Math. Optim., 67 (2013), 391-418.       
8 A. Lorenzi, Severely ill-posed linear parabolic integrodifferential problems, J. Inverse Ill-Posed Probl., (2012).
9 A. Lorenzi, Recovering a t-function in a strongly ill-posed integro-differential parabolic problem with integral boundary conditions, to appear in Mathematical Modelling and Analysis.
10 A. Lorenzi and L. Lorenzi, A strongly ill-posed problem for a degenerate parabolic equation with unbounded coefficients in an unbounded domain $\Omega\times \mathcal O$ of $\mathbb R^{M+N}$, Inverse Problems, 29 (2013), 025007, 22 pp.       
11 A. Lorenzi and F. Messina, Unique continuation and continuous dependence results for a strongly ill-posed integro-differential parabolic problem, J. Inverse Ill-Posed Probl., 20 (2012), 615-636.       
12 A. Lorenzi and I. Munteanu, Recovering a constant in the two-dimensional Navier-Stokes system with no initial condition, to appear in Applied Mathematics and Optimization.
13 A. Lorenzi and M. Yamamoto, Continuous dependence and uniqueness for a strongly ill-posed problem for linear integrodifferential parabolic equations, in progress.

Go to top