Existence of global solution of a nonlinear wave equation with short-range potential

• Autorzy: V. Georgiev , K. Ianakiev
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1992
• Tom: 27
• Numer: 1
• Strony: 163-167

Daty

wydano

1992

Twórcy

autor

V. Georgiev

• Section of Mathematical Physics, Institute of Mathematics, Bulgarian Academy of Sciences, Acad. G. Bonchev str. bl. 8, 1113 Sofia, Bulgaria

autor

K. Ianakiev

• Section of Mathematical Physics, Institute of Mathematics, Bulgarian Academy of Sciences, Acad. G. Bonchev str. bl. 8, 1113 Sofia, Bulgaria

Bibliografia

• [1] P. Datti, Long time existence of classical solutions to a non-linear wave equation in exterior domains, Ph.D. Dissertation, New York University, 1985.
• [2] P. Godin, Long time behaviour of solutions to some nonlinear rotation invariant mixed problems, Comm. Partial Differential Equations 14 (3) (1989), 299-374.
• [3] L. Hörmander, The Analysis of Linear Partial Differential Operators, Vol. I, Distribution Theory and Fourier Analysis, Springer, New York 1983.
• [4] L. Hörmander, Non-linear Hyperbolic Differential Equations, Lectures 1986-1987, Lund 1988.
• [5] F. John, Blow-up for quasi-linear wave equations in three space dimensions, Comm. Pure Appl. Math. 34 (1981), 20-51.
• [6] S. Klainerman, The null condition and global existence to nonlinear wave equations, in: Lectures in Appl. Math. 23, Part 1, Amer. Math. Soc., Providence, R.I., 1986, 293-326.
• [7] S. Klainerman, Uniform decay estimates and the Lorentz invariance of the classical wave equation, Comm. Pure Appl. Math. 38 (1985), 321-332.
• [8] C. Morawetz, Energy decay for star-shaped obstacles, Appendix 3 in: P. Lax and R. Phillips, Scattering Theory, Academic Press, New York 1967.
• [9] H. Pecher, Scattering for semilinear wave equations with small initial data in three space dimensions, Math. Z. 198 (1988), 277-288.
• [10] Y. Shibata and Y. Tsutsumi, On global existence theorem of small amplitude solutions for nonlinear wave equations in exterior domains, ibid. 191 (1986), 165-199.