Show simple item record

dc.contributor.advisorHanmehmetli, Azer
dc.contributor.authorŞen, Zehra
dc.date.accessioned2018-05-22T07:08:03Z
dc.date.available2018-05-22T07:08:03Z
dc.date.issued2018
dc.date.submitted2018-05-11
dc.identifier.citation[1] Kalantarov, V., Attractors for some nonlinear problems of mathematical physics, Zapiski Nauchnykh Seminarov Leningradskogo 0tdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, (LOMI), (LOMI) 152, 50-54, 1986. [2] Ghidaglia, J.M., Marzocchi, A., Longtime behaviour of strongly damped wave equations, global attractors and their dimension, SIAM Journal of Mathematical Analysis, 22, 879-895, 1991. [3] Zhou, S., Global attractor for strongly damped nonlinear wave equations, Functional Differential Equations, 6, 451-470, 1999. [4] Carvalho, A.N., Cholewa, JW., Attractors for strongly damped wave equations with critical nonlinearities, Paci c Journal of Mathematics, 207, 287-310, 2002. [5] Pata, V., Squassina, M., On the strongly damped wave equation, Communications in Mathematical Physics, 253, 511-533, 2005. [6] Pata, V., Zelik, S., Smooth attractors for strongly damped wave equations, Nonlinearity, 19, 1495-1506, 2006. [7] Yang, M., Sun, C., Attractors for strongly damped wave equations, Nonlinear Analysis: Real World Applications, 10, 1097-1100, 2009. [8] Dell'Oro, F., Pata, V., Long-term analysis of strongly damped nonlinear wave equations, Nonlinearity, 24, 3413-3435, 2011. [9] Dell'Oro, F., Pata, V., Strongly damped wave equations with critical nonlinearities, Nonlinear Analysis, 75, 5723-5735, 2012. [10] Khanmamedov, AK., Global attractors for strongly damped wave equations with displacement dependent damping and nonlinear source term of critical exponent, Discrete and Continuous Dynamical Systems. Series A, 31, 119-138, 2011. [11] Khanmamedov, AK., Strongly damped wave equation with exponential nonlinearities, Journal of Mathematical Analysis and Applications, 419, 663-687, 2014. 103 [12] Khanmamedov, AK., On the existence of a global attractor for the wave equation with nonlinear strong damping perturbed by nonmonotone term, Nonlinear Analysis, 69, 3372-3385, 2008. [13] Chueshov, I., Lasiecka, I., Long time behavior of second order evolution equations with nonlinear damping, Memoirs of the American Mathematical Society, 195, 2008. [14] Chen, F., Guo, B., Wang, P., Long time behavior of strongly damped nonlinear wave equations, Journal of Differential Equations, 147, 231-241, 1998. [15] Kalantarov, V., Zelik, S., Finite-dimensional attractors for the quasi-linear strongly-damped wave equation, Journal of Differential Equations, 247, 1120-1155, 2009. [16] Arat Z., Khanmamedov, AK., Simsek, S., Global attractors for the plate equation with nonlocal nonlinearity in unbounded domains, Dynamics of Partial Differential Equations, 11, 361-379, 2014. [17] Arat Z., Khanmamedov, AK., Simsek, S., A unique continuation result for the plate equation and an application, Mathematical Methods in the Applied Sciences, 39, 744-761, 2016. [18] Ball, J.M., Global attractors for semilinear wave equations, Discrete and Continuous Dynamical Systems. Series A, 10, 31-52, 2004. [19] Khanmamedov, AK., Global attractors for von Karman equations with nonlinear interior dissipation, Journal of Mathematical Analysis and Applications, 318, 92- 101, 2006. [20] Khanmamedov, AK., S en, Z., Attractors for the Strongly Damped Wave Equation with p-Laplacian, Mathematical Methods in the Applied Sciences, 40, 4436-4447, 2017. [21] Zeidler, E., Nonlinear Functional Analysis and Its Applications: I: Fixed-Point Theorems, Springer, 1985. [22] Adams, R.A., Sobolev Spaces, Academic Press, New York, 1975. 104 [23] Zeidler, E., Nonlinear Functional Analysis and Its Applications: II/ A: Linear Monotone Operators, Springer, 1989. [24] Royden, H.L., Real Analysis, Macmillan, New York, 1968. [25] Showalter, R.E. , Monotone Operators in Banach Space and Nonlinear Partial Di erential Equations, American Mathematical Society, 1997. [26] Porter, D., Stirling, David S.G., Integral Equations: A Practical Treatment, from Spectral Theory to Applications (Cambridge Texts in Applied Mathematics), 1990. [27] Chueshov, I., Lasiecka, I., Von Karman Evolution Equations:Well-posedness and long-time dynamics, Springer: New York, 2010. [28] Kesevan, S., Topics in functional analysis and applications, Wiley, 1989. [29] Lions, J.L., Magenes, E., Non-Homogeneous Boundary Value Problems and Applications I, Springer Berlin Heidelberg, 1972. [30] Agronovich, M.S., Sobolev Spaces, Their Generalizations, and Elliptic Problems in Smooth and Lipschitz Domains, Springer, Heidelberg, 2015. [31] Babin, A.V., Vishik, M.I., Attractors for evolution equations, North-Holland, Amsterdam, 1992. [32] Larsson, S., Thomee, V., Partial Differential Equations with Numerical Methods, Springer-Verlag Berlin Heidelberg, 1st edition, 2003. [33] Lusternik, L.A., Sobolev, V.J., Elements of Functional Analysis, John Wiley & Sons, New York, 1961. [34] Cazenave, T., Haraux, A., An Introduction to Semilinear Evolution Equations, Clarandon Press Oxford, 1998. [35] Evans, C., Partial Differential Equations, Graduate studies in Mathematics, Vol 19, AMS, 1998.tr_TR
dc.identifier.urihttp://hdl.handle.net/11655/4488
dc.description.abstractIn this thesis, we concern the long time behaviours of the one dimensional strongly damped nonlinear wave equation u_tt-u_txx-∂/∂x (|u_x |^(p-2) u_x )+f(u)=g(x) (1) in bounded domain and the one dimensional strongly damped nonlinear wave equation with localized damping term u_tt-u_txx-u_xx-∂/∂x (|u_x |^(p-2) u_x )+a(x) u_t+f(u)=g(x) (2) in unbounded domain. The thesis consists of four sections. In the first section, the previous studies about the long time dynamics of the strongly damped wave equations and the main purpose of the thesis are mentioned. Second section is devoted to the main theorems and definitions. In the third section, we prove the well-posedness of the initial boundary value problem for equation (1) and the existence of regular strong global attractor in W_0^(1,p)(0,1)×L^2(0,1) for the semigroup generated by the problem. In the fourth section, we obtain the well-posedness of the initial value problem for equation (2) and the existence of weak local attractors in (W^(1,p)(R)∩H^1(R))×L^2(R) for the semigroup generated by the problem.tr_TR
dc.description.tableofcontentsÖzet, Abstract, Teşekkür, İçindekiler Dizini, Giriş, Ön Bilgiler ve Temel Teoremler, Sınırlı Bölgede Doğrusal Olmayan Dalga Denkleminin Çekicisi, Sınırlı Olmayan Bölgede Yerel Sönüm Terimine Sahip Doğrusal Olmayan Dalga Denkleminin Çekicisi, Kaynaklar, Özgeçmiştr_TR
dc.language.isoturtr_TR
dc.publisherFen Bilimleri Enstitüsütr_TR
dc.rightsinfo:eu-repo/semantics/openAccesstr_TR
dc.subjectDalga Denklemi
dc.subjectP-Laplacian
dc.subjectÇekiciler
dc.titleKuasilineer Dalga Denkleminin Uzun Zaman Davranışıtr_TR
dc.typeinfo:eu-repo/semantics/doctoralThesistr_TR
dc.description.ozetBu tezde, sınırlı bölgede, bir boyutlu kuvvetli sönümlü doğrusal olmayan u_tt-u_txx-∂/∂x (|u_x |^(p-2) u_x )+f(u)=g(x) (1) dalga denklemi ile sınırlı olmayan bölgede, yerel sönüm terimine sahip, bir boyutlu kuvvetli sönümlü doğrusal olmayan u_tt-u_txx-u_xx-∂/∂x (|u_x |^(p-2) u_x )+a(x) u_t+f(u)=g(x) (2) dalga denkleminin uzun zaman davranışı ele alınmıştır. Bu çalışma dört bölümden oluşmaktadır. Birinci bölümde, kuvvetli sönümlü dalga denklemlerinin uzun zaman dinamikleri ile ilgili yapılmış çalışmalara ve tezin amacına yer verilmiştir. İkinci bölüm ise, tezde kullanılacak temele teoremlere ve tanımlara ayrılmıştır. Üçüncü bölümde, (1) denklemi için ele aldığımız başlangıç sınır değer probleminin iyi konulmuş bir problem olduğu gösterilmiş ve bu problemin ürettiği yarı grubun W_0^(1,p)(0,1)×L^2(0,1)'de düzgün kuvvetli yerel olmayan çekiciye sahip olduğu ispatlanmıştır. Dördüncü bölümde ise, (2) denklemi için incelenen başlangıç değer probleminin iyi konulmuş bir problem olduğu elde edilmiş ve bu problemin ürettiği yarı grubun (W^(1,p)(R)∩H^1(R))×L^2(R)'de zayıf yerel çekicilere sahip olduğu gösterilmiştir.tr_TR
dc.contributor.departmentMatematiktr_TR
dc.contributor.authorID170378tr_TR


Files in this item

This item appears in the following Collection(s)

Show simple item record