Long-time Behaviour of Solution to Inverse Problem for Higher-order Parabolic Equation

Year 2019, Volume: 23 Issue: 4, 696 - 699, 01.08.2019

Metin Yaman

https://doi.org/10.16984/saufenbilder.516390

Abstract

We consider an inverse problem for the fourth-order
parabolic equation. Long time behavior of the solution for the higher-order
nonlinear inverse problem is established. Additional condition is given in the
form of integral overdetermination.

Keywords

long-time behavior, integral overdetermination, higher-order parabolic equation, inverse problem

References

• [1] A.I.Prilepko, D.G.Orlovsky, I.A.Vasin, Methods for solving inverse problems in mathematical physics, Marcel Dekker, 1999.
• [2] A.G.Ramm, Inverse problems, Mathematical and Analytical Techniques with Applications to Engineering. Springer, New York, (2000).
• [3] M.Yaman, “Parabolik denklemler için ters problemin çözümünün asimptotik davranışı”, Doktora tezi, Sakarya Üniversitesi Fen Bilimleri Enstitüsü, 2002.
• [4] I.A.Vasin, V.L.Kamynin, "On the asymtotic behavior of solutions of inverse problems for parabolic equations", Siberian Math. Journal, 38, 647-662, 1997.
• [5]V.L.Kamynin, “On the unique solvability of an inverse problem for parabolic equations under a final overdetermination condition”, Math. Notes, vol.73, no.2, 202-211, 2003.
• [6] H.Kocaman, M.Yaman, “Finite time blow up of solutions to fourth-order equation with power nonlinearity” ISITES 2015 Valencia–Spain, 2508-2515.
• [7] M.Yaman, “Blow up of solutions to an inverse problem for a quasilinear parabolic equation”, ISITES 2015 Valencia–Spain, 1366-1375.
• [8] V. L. Kamynin, E. Franchini, “An inverse problem for a higher-order parabolic equation”, Mathematical Notes , 1998, vol.64, no.5, 590-599.
• [9] F. Tahamtani, M. Shahrouzi, Asymptotic stability and blow up of solutions for a Petrovsky inverse source problem with dissipative boundary condition, Math. Meth. Appl. Sci. 2013, 36, 829–839
• [10] Huafei Di Yadong Shang, Blow up of solutions for a class of fourth order nonlinear pseudo-parabolic equation with a nonlocal source, Boundary value problems, 2015:109.
• [11] Jun Zhou “L2-norm blow-up of solutions to a fourth order parabolic PDE involving the Hessian”, J. Differential Equations, 265, 4632–4641, 2018.