Wellposedness of bounded solutions of the non-homogeneous initial boundary for the short pulse equation

被引:19
作者
Coclite G.M. [1 ]
Di Ruvo L. [1 ]
机构
[1] Department of Mathematics, University of Bari, via E. Orabona 4, Bari
关键词
Boundary value problems; Conservation laws; Entropy solutions; Existence; Short pulse equation; Stability; Uniqueness;
D O I
10.1007/s40574-015-0023-3
中图分类号
学科分类号
摘要
The short pulse equation provides a model for the propagation of ultra-short light pulses in silica optical fibers. It is a nonlinear evolution equation. In this paper the wellposedness of bounded solutions for the inhomogeneous initial boundary value problem associated to this equation is studied. © 2015 Unione Matematica Italiana.
引用
收藏
页码:31 / 44
页数:13
相关论文
共 24 条
[1]  
Amiranashvili S., Vladimirov A.G., Bandelow U., A model equation for ultrashort optical pulses, Eur. Phys. J. D, 58, (2010)
[2]  
Bardos C., Leroux A.Y., Nedelec J.C., First order quasilinear equations with boundary conditions, Comm. Partial Differ. Equ., 4, 9, pp. 1017-1034, (1979)
[3]  
Boyd R.W., Nonlinear Optics, (1992)
[4]  
Brunelli J.C., The short pulse hierarchy, J. Math. Phys., 46, (2005)
[5]  
Chung Y., Jones C., Schafer T., Wayne C.E., Ultra-short pulses in linear and nonlinear media, Nonlinearity, 18, pp. 1351-1374, (2005)
[6]  
Coclite G. . M., Di Ruvo L., Wellposedness of bounded solutions of the non-homogeneous initial boundary value problem for the Ostrovsky-Hunter equation, J. Hyperbolic Differ. Equ.
[7]  
Coclite G. . M., Di Ruvo L., Wellposedness results for the short pulse equation, Z. Angew. Math. Phys.
[8]  
Coclite G. . M., Di Ruvo L., Convergence of the Regularized Short Pulse Equation to the Short Pulse One
[9]  
Coclite G. . M., Di Ruvo L., Karlsen K. . H., Some wellposedness results for the Ostrovsky-Hunter equation, Proceedings of Hyperbolic Conservation Laws and Related Analysis with Applications, 143-159, Springer Proc. Math. Stat., (2014)
[10]  
Coclite G.M., Holden H., Karlsen K.H., Wellposedness for a parabolic-elliptic system, Discret. Contin. Dyn. Syst., 13, 3, pp. 659-682, (2005)