Backward solutions to nonlinear integro-differential systems

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1. [1] Amadori A.L., Nonlinear integro-differential evolution problems arising in option pricing: a viscosity solutions approach, Differential Integral Equations, 2003, 16(7), 787–811 Zbl1052.35083
2. [2] Dafermos C.M., An abstract Volterra equation with application to linear viscoelasticity, J. Differential Equations, 1970, 7, 554–569 http://dx.doi.org/10.1016/0022-0396(70)90101-4[Crossref] 
3. [3] Dzhangveladze T.A., The first boundary value problem for a nonlinear equation of parabolic type, Soviet Phys. Dokl., 1983, 28(4), 323–324 Zbl0538.35045
4. [4] Dzhangveladze T.A., A nonlinear integro-differential equation of parabolic type, Differ. Equ., 1985, 21, 32–36 Zbl0595.45022
5. [5] Dzhangveladze T.A., Kiguradze Z.V., On the stabilization of solutions of an initial-boundary value problem for a nonlinear integro-differential equation, Diff. Equ., 2007, 43(6), 854–861 http://dx.doi.org/10.1134/S0012266107060110[Crossref] Zbl1136.78018
6. [6] Dzhangveladze T.A., Kiguradze Z.V., Asymptotic behavior of the solution of a nonlinear integrodifferential diffusion equation, Diff. Equ., 2008, 44(4), 538–550 http://dx.doi.org/10.1134/S0012266108040083[Crossref] Zbl1172.35500
7. [7] Engler H., On Some Parabolic Integro-Differential Equations: Existence and Asymptotics of Solutions, Lecture Notes in Math., 1017, Springer, Berlin, 1983 
8. [8] Engler H., Global smooth solutions for a class of parabolic integrodifferential equations, Trans. Amer. Math. Soc., 1996, 348(1), 267–290 http://dx.doi.org/10.1090/S0002-9947-96-01472-9[Crossref] Zbl0848.45002
9. [9] Evans L.C., Partial Differential Equations, Graduate Studies in Mathematics, 19, American Mathematical Society, Providence, 1998 Zbl0902.35002
10. [10] Fila M., Pulkkinen A., Backward selfsimilar solutions of supercritical parabolic equations, Appl. Math. Lett., 2009, 22(6), 897–901 http://dx.doi.org/10.1016/j.aml.2008.07.018[Crossref] Zbl1173.35547
11. [11] Gordeziani D.G., Dzhangveladze T.A., Korshiya T.K., Existence and uniqueness of the solution of a class of nonlinear parabolic problems, Diff. Equ., 1983, 19, 887–895 Zbl0582.35065
12. [12] Gripenberg G., Global existence of solutions of Volterra integro-differential equations of parabolic type, J. Differential Equations, 1993, 102(2), 382–390 http://dx.doi.org/10.1006/jdeq.1993.1035[Crossref] 
13. [13] Hoff D., Tsyganov E., Time analyticity and backward uniqueness of weak solutions of the Navier-Stokes equations of multidimensional compressible flow, J. Differential Equations, 2008, 245(10), 3068–3094 http://dx.doi.org/10.1016/j.jde.2008.08.006[Crossref][WoS] Zbl05365162
14. [14] Jangveladze T.A., Kiguradze Z.V., Asymptotics of a solution of a nonlinear system of diffusion of a magnetic field into a substance, Siberian Math. J., 2006, 47(5), 867–878 http://dx.doi.org/10.1007/s11202-006-0095-5[Crossref] Zbl1150.45316
15. [15] Jangveladze T., Kiguradze Z., Neta B., Large time behavior of solutions to a nonlinear integro-differential system, J. Math. Anal. Appl., 2009, 351(1), 382–391 http://dx.doi.org/10.1016/j.jmaa.2008.10.016[Crossref] Zbl1172.35330
16. [16] Lions J.-L., Magenes E., Non-homogeneous Boundary Value Problems and Applications, Vol. 1, Springer, Berlin, 1972 Zbl0223.35039
17. [17] Renardy M., Hrusa W.J., Nohel J.A., Mathematical Problems in Viscoelasticity, Wiley&Sons, New York, 1987 Zbl0719.73013