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Solvability, continuous dependence and asymptotic expansion of solutions in a small parameter of Dirichlet problem for a nonlinear Kirchhoff wave equation | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 2، دوره 14، شماره 9، آذر 2023، صفحه 17-46 اصل مقاله (615.72 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.30205.4362 | ||
| نویسندگان | ||
| Le Huu Ky Son1؛ Ly Anh Duong2، 3؛ Le Thi Phuong Ngoc4؛ Nguyen Thanh Long* 2، 3 | ||
| 1Faculty of Applied Sciences, Ho Chi Minh City University of Food Industry, 140 Le Trong Tan Str., Tan Phu Dist., Ho Chi Minh City, Vietnam | ||
| 2Faculty of Mathematics and Computer Science, University of Science, Ho Chi Minh City, 227 Nguyen Van Cu Str., Dist. 5, Ho Chi Minh City, Vietnam | ||
| 3Vietnam National University, Ho Chi Minh City, Vietnam | ||
| 4University of Khanh Hoa, 01 Nguyen Chanh Str., Nha Trang City, Vietnam | ||
| تاریخ دریافت: 24 اسفند 1401، تاریخ پذیرش: 31 خرداد 1402 | ||
| چکیده | ||
| We study the existence, uniqueness, continuous dependence, and asymptotic expansion of solutions of the Dirichlet problem for a nonlinear Kirchhoff wave equation. At first, we state and prove a theorem involving the local existence and uniqueness of a weak solution. Next, we establish a sufficient condition to get an estimate of the continuous dependence of the solution with respect to the nonlinear terms. Finally, an asymptotic expansion of high order in a small parameter of a weak solution is also discussed. | ||
| کلیدواژه‌ها | ||
| Faedo-Galerkin method؛ Linear recurrent sequence؛ Continuous dependence؛ Asymptotic expansion | ||
| مراجع | ||
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[1] M.M. Cavalcantia, V.N. Domingos Cavalcanti, and P. Martinez, General decay rate estimates for viscoelastic dissipative systems, Nonlinear Anal. TMA. 68 (2008), 177–193. [2] M. D’Abbicco, The influence of a nonlinear memory on the damped wave equation, Nonlinear Anal. TMA. 95 (2014), 130–145. [3] M. D’Abbicco and S. Lucente, The beam equation with nonlinear memory, Z. Angew. Math. Phys. 67 (2016), 1–18. [4] A. Douglis, The continuous dependence of generalized solutions of nonlinear partial differential equations upon initial data, Commun. Pure Appl. Math. 14 (1961), 267–284. [5] G. Duvaut and J.L. Lions, Inequalities in Mechanics and Physics, 1st ed., Springer-Verlag Berlin Heidelberg, 1976. [6] F. Ekinci, E. Piskin, S.M. Boulaaras, and I. Mekawy, Global existence and general decay of solutions for a quasilinear system with degenerate damping terms, J. Funct. Spaces 2021 (2021), Article ID: 4316238, 10 pages. [7] A. Fino, Critical exponent for damped wave equations with nonlinear memory, Nonlinear Anal. 74 (2011), 5495–5505. [8] J. Fritz, Continuous dependence on data for solutions of partial differential equations with a prescribed bound, Commun. Pure Appl. Math. 13 (1960), 551–586. [9] X. Han and M. Wang, General decay of energy for a viscoelastic equation with nonlinear damping, J. Franklin Inst. 347 (2010), 806–817. [10] J. Hao and H. Wei, Blow-up and global existence for solution of quasilinear viscoelastic wave equation with strong damping and source term, Bound. Value Probl. 2017 (2017), no. 65. [11] T.H. Kaddour and M. Reissig, Global well-posedness for effectively damped wave models with nonlinear memory, Commun. Pure Appl. Anal. 20 (2021), 2039–2064. [12] M. Kafini and S.A. Messaoudi, A blow-up result in a Cauchy viscoelastic problem, Appl. Math. Lett. 21 (2008), 549–553. [13] M. Kafini and M.I. Mustafa, Blow-up result in a Cauchy viscoelastic problem with strong damping and dispersive, Nonlinear Anal. RWA. 20 (2014), 14–20. [14] G.R. Kirchhoff, Vorlesungen ¨uber Mathematische Physik, Mechanik, Teubner, Leipzig, 1876. [15] Q. Li and L. He, General decay and blow-up of solutions for a nonlinear viscoelastic wave equation with strong damping, Bound. Value Probl. 2018 (2018), no. 153. [16] J.L. Lions, Quelques Methodes de Resolution des Problemes Aux limites Nonlineaires, Dunod, Gauthier-Villars, Paris, 1969. [17] N.T. Long, On the nonlinear wave equation utt −B(t, ||u||2 , ||ux||2)uxx = f(x, t, u, ux, ut, ||u||2 , ||ux||2) associated with the mixed homogeneous conditions, J. Math. Anal. Appl. 306 (2005), no. 1, 243–268. [18] F. Mesloub and S. Boulaaras, General decay for a viscoelastic problem with not necessarily decreasing kernel, J. Appl. Math. Comput. 58 (2018), 647–665. [19] S.A. Messaoudi, Blow-up and global existence in a nonlinear viscoelastic wave equation, Math. Nachr. 260 (2003), 58–66. [20] S.A. Messaoudi, General decay of the solution energy in a viscoelastic equation with a nonlinear source, Nonlinear Anal. TMA. 69 (2008), 2589–2598. [21] M.I. Mustafa, Optimal decay rates for the viscoelastic wave equation, Math. Meth. Appl. Sci. 41 (2018), 192–204. [22] M. Nakao, A difference inequality and its application to nonlinear evolution equations, J. Math. Soc. Japan 30 (1978), 747–762. [23] L.T.P. Ngoc, D.T.N. Quynh, N.A. Triet, and N.T. Long, Linear approximation and asymptotic expansion associated to the Robin-Dirichlet problem for a Kirchhoff-Carrier equation with a viscoelastic term, Kyungpook Math. J. 59 (2019) 735-769. [24] K. Ono, Global existence, decay, and blowup of solutions for some mildly degenerate nonlinear Kirchhoff strings, J. Diff. Eqns. 137 (1997), 273–301. [25] K. Ono, On global existence, asymptotic stability and blowing up of solutions for some degenerate nonlinear wave equations of Kirchhoff type with a strong dissipation, Math. Meth. Appl. Sci. 20 (1997), 151–177. [26] K. Ono, On global solutions and blow-up solutions of nonlinear Kirchhoff strings with nonlinear dissipation, J. Math. Anal. Appl. 216 (1997), 321–342. [27] D.T.N. Quynh, N.H. Nhan, L.T.P. Ngoc, and N.T. Long, Continuous dependence and general decay of solutions for a wave equation with a nonlinear memory term, Appl. Math. 68 (2023), no. 2, 209–254. | ||
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