Existence and exponential decay estimates for an N-dimensional nonlinear wave equation with a nonlocal boundary condition

被引：0
作者：
Le Thi Phuong Ngoc
Nguyen Anh Triet
Nguyen Thanh Long
机构：
[1] University of Khanh Hoa,Department of Mathematics
[2] University of Architecture of Ho Chi Minh City,Department of Mathematics and Computer Science
[3] University of Natural Science,undefined
[4] Vietnam National University Ho Chi Minh City,undefined
来源：
Boundary Value Problems | / 2016卷
关键词：
Galerkin method; nonlinear wave equation; local existence; global existence; exponential decay; 35L05; 35L15; 35L70; 37B25;
D O I：
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摘要：
Motivated by the recent known results as regards the existence and exponential decay of solutions for wave equations, this paper is devoted to the study of an N-dimensional nonlinear wave equation with a nonlocal boundary condition. We first state two local existence theorems. Next, we give a sufficient condition to guarantee the global existence and exponential decay of weak solutions. The main tools are the Faedo-Galerkin method and the Lyapunov method.
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  • [1] Guezane-Lakoud A(2011)Existence and uniqueness of generalized solutions to a telegraph equation with an integral boundary condition via Galerkin’s method Int. J. Math. Math. Sci. 2011 547-561
  • [2] Dabas J(2001)Mathematical model for a shock problem involving a linear viscoelastic bar Nonlinear Anal. TMA 43 391-399
  • [3] Bahuguna D(2006)On a mixed nonlocal problem for a wave equation Electron. J. Differ. Equ. 2006 533-548
  • [4] Bergounioux M(2005)Exponential decay of solutions of a nonlinearly damped wave equation Nonlinear Differ. Equ. Appl. 12 613-623
  • [5] Long NT(1998)Global classical solutions to the Cauchy problem for a nonlinear wave equation Int. J. Math. Math. Sci. 21 1070-1093
  • [6] Dinh APN(1992)On the quasilinear wave equation: Nonlinear Anal. TMA 19 337-358
  • [7] Beilin SA(2012) associated with a mixed nonhomogeneous condition J. Math. Anal. Appl. 385 842-864
  • [8] Benaissa A(2005)On a nonlinear wave equation with boundary conditions of two-point type Bound. Value Probl. 2005 63-68
  • [9] Messaoudi SA(2007)On a shock problem involving a nonlinear viscoelastic bar Nonlinear Anal. TMA 67 91-127
  • [10] Clark HR(2001)Existence and asymptotic expansion for a viscoelastic problem with a mixed nonhomogeneous condition Arab. J. Sci. Eng. 26 211-263
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