Research Article
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Year 2019, , 696 - 699, 01.08.2019
https://doi.org/10.16984/saufenbilder.516390

Abstract

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.

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

Year 2019, , 696 - 699, 01.08.2019
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.

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.
There are 11 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Metin Yaman 0000-0003-2208-5730

Publication Date August 1, 2019
Submission Date January 22, 2019
Acceptance Date February 21, 2019
Published in Issue Year 2019

Cite

APA Yaman, M. (2019). Long-time Behaviour of Solution to Inverse Problem for Higher-order Parabolic Equation. Sakarya University Journal of Science, 23(4), 696-699. https://doi.org/10.16984/saufenbilder.516390
AMA Yaman M. Long-time Behaviour of Solution to Inverse Problem for Higher-order Parabolic Equation. SAUJS. August 2019;23(4):696-699. doi:10.16984/saufenbilder.516390
Chicago Yaman, Metin. “Long-Time Behaviour of Solution to Inverse Problem for Higher-Order Parabolic Equation”. Sakarya University Journal of Science 23, no. 4 (August 2019): 696-99. https://doi.org/10.16984/saufenbilder.516390.
EndNote Yaman M (August 1, 2019) Long-time Behaviour of Solution to Inverse Problem for Higher-order Parabolic Equation. Sakarya University Journal of Science 23 4 696–699.
IEEE M. Yaman, “Long-time Behaviour of Solution to Inverse Problem for Higher-order Parabolic Equation”, SAUJS, vol. 23, no. 4, pp. 696–699, 2019, doi: 10.16984/saufenbilder.516390.
ISNAD Yaman, Metin. “Long-Time Behaviour of Solution to Inverse Problem for Higher-Order Parabolic Equation”. Sakarya University Journal of Science 23/4 (August 2019), 696-699. https://doi.org/10.16984/saufenbilder.516390.
JAMA Yaman M. Long-time Behaviour of Solution to Inverse Problem for Higher-order Parabolic Equation. SAUJS. 2019;23:696–699.
MLA Yaman, Metin. “Long-Time Behaviour of Solution to Inverse Problem for Higher-Order Parabolic Equation”. Sakarya University Journal of Science, vol. 23, no. 4, 2019, pp. 696-9, doi:10.16984/saufenbilder.516390.
Vancouver Yaman M. Long-time Behaviour of Solution to Inverse Problem for Higher-order Parabolic Equation. SAUJS. 2019;23(4):696-9.

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