Global existence and decay estimate of the solution for a BBM-Burgers equation without viscosity
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摘要: 本文通过构造柯西逼近序列证明了一类无粘BBM-Burgers方程解的局部存在性和衰减估计, 应用常数变易公式结合基本解的衰减估计证明了小初值条件下解的整体存在性, 并得到了衰减估计.
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关键词:
- BBM-Burgers方程 /
- 柯西问题 /
- 解的整体存在性 /
- 衰减估计
Abstract: By constructing a Cauchy approximating sequence, we prove the local existence and give the decay estimate of the solution for a BBM-Burgers equation without viscosity. Using the variation of constant formula and the decay estimate of the fundamental solution, we obtain the global existence and decay estimate of solution of the system with small initial data. -
[1] [ 1 ] BENJAMIN T B, BONA J L, MAHONY J J. Model equations for long waves in nonlinear dispersive system [J]. Phil Trans R, 1972, 272: 47-78.
[ 2 ] MEDEIROS L A, MENZALA P G. Existence and uniqueness for periodic solutions of the Benjamin-Bona-Mahony equation [J]. Siam Journal on Mathematical Analysis, 1977, 8(5): 792-799.
[ 3 ] AVRIN J. The generalized Benjamin-Bona-Mahony equation in Rn with singular initial data [J]. Nonlinear Analysis, 1987, 11(1): 139-147.
[ 4 ] BILER P. Long time behavior of solutions of the generalized Benjamin-Bona-Mahony equation in two space dimensions [J]. Differential and Integral Equations, 1992, 5(4): 891-901.
[ 5 ] FANG S, GUO B. The decay rates of solutions of generalized Benjamin-Bona-Mahony equations in multi-dimensions [J]. Nonlinear Analysis, 2008, 69: 2230-2235.
[ 6 ] ZHANG L H. Decay of solutions of generalized Benjamin-Bona-Mahony equations [J]. Acta Mathematica Sinica,1994, 10(4): 428-438.
[ 7 ] ZHAO H J. Optimal temporal decay estimates for the solution to the multidimensional generalized BBM-Burgers equations with dissipative term [J]. Applicable Analysis, 2000, 75(1/2): 85-105.
[ 8 ] ZHAO H J, XUAN B J. Existence and convergence of solutions for the generalized BBM-Burgers equations with dissipative term [J]. Nonlinear Analysis, 1997, 28(11): 1835-1849.
[ 9 ] ZHAO H J, ADMAS R A. Existence and convergence of solutions for the generalized BBM-burgers equations with dissipative term 2: The multidimensional case [J]. History and Philosophy of Logic, 2000, 75(1): 107-135.
[10] WANG W K, ZHANG D D. Large-time behavior for the solution to the generalized Benjamin-Bona-Mahony-Burgers equation with larger initial data in the whole space [J]. Journal of Mathematical Analysis and Applications, 2014, 411(1): 144-165.
[11] LI D Q, CHEN Y M. Nonlinear Evolution Equation [M]. Beijing: Science Press, 1989. -
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