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GLOBAL SOLUTIONS OF THE EXPONENTIAL WAVE EQUATION WITH SMALL INITIAL DATA
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 Title & Authors
GLOBAL SOLUTIONS OF THE EXPONENTIAL WAVE EQUATION WITH SMALL INITIAL DATA
Huh, Hyungjin;
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 Abstract
We study the initial value problem of the exponential wave equation in for small initial data. We shows, in the case of , the global existence of solution by applying the formulation of first order quasilinear hyperbolic system which is weakly linearly degenerate. When , a vector field method is applied to show the stability of a trivial solution .
 Keywords
quasilinear wave;weakly linearly degenerate;double null form;
 Language
English
 Cited by
1.
Global existence of smooth solutions to exponential wave maps in FLRW spacetimes, Pacific Journal of Mathematics, 2017, 289, 2, 489  crossref(new windwow)
 References
1.
S. Alinhac, Hyperbolic Partial Differential Equations, Universitext, Springer, Dordrecht, 2009.

2.
Y.-J. Chiang and Y.-H. Yang, Exponential wave maps, J. Geom. Phys. 57, (2007) no. 12, 2521-2532. crossref(new window)

3.
J. Eells and L. Lemaire, Another report on harmonic maps, Bull. London Math. Soc. 20 (1988), no. 5, 385-524. crossref(new window)

4.
J. Eells and L. Lemaire, Some properties of exponentially harmonic maps, Partial differential equations, Part 1, 2 (Warsaw, 1990), 129-136, Banach Center Publ., 27, Part 1, 2, Polish Acad. Sci., Warsaw, 1992.

5.
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer Verlag, 1977.

6.
L. Hormander, Lectures on Nonlinear Hyperbolic Differential Equations, Springer Verlag, 1997.

7.
F. John, Formation of singularities in one-dimensional nonlinear wave propagation, Comm. Pure Appl. Math. 27 (1974), 377-405. crossref(new window)

8.
A. D. Kanfon, A. Fuzfa, and D. Lambert, Some examples of exponentially harmonic maps, J. Phys. A 35 (2002), no. 35, 7629-7639. crossref(new window)

9.
S. Klainerman, The null condition and global existence to nonlinear wave equations, Nonlinear systems of partial differential equations in applied mathematics, Part 1 (Santa Fe, N.M., 1984), 293-326, Lectures in Appl. Math., 23, Amer. Math. Soc., Providence, RI, 1986.

10.
D. Kong, Cauchy Problem for Quasilinear Hyperbolic Systems, MSJ Memoirs, 6. Mathematical Society of Japan, Tokyo, 2000.

11.
T.-T. Li, Y. Zhou, and D. Kong, Global classical solutions for general quasilinear hyperbolic systems with decay initial data, Nonlinear Anal. 28 (1997), no. 8, 1299-1332. crossref(new window)

12.
H. Lindblad, On the lifespan of solutions of nonlinear wave equations with small initial data, Comm. Pure Appl. Math. 43 (1990), no. 4, 445-472. crossref(new window)

13.
H. Lindblad, A remark on global existence for small initial data of the minimal surface equation in Minkowskian space time, Proc. Amer. Math. Soc. 132 (2004), no. 4, 1095-1102. crossref(new window)

14.
M. C. Hong, Liouville theorems for exponentially harmonic functions on Riemannian manifolds, Manuscripta Math. 77 (1992), no. 1, 41-46. crossref(new window)

15.
J. M. Overduin and P. S. Wesson, Kaluza-Klein gravity, Phys. Rep. 283 (1997), no. 5-6, 303-378. crossref(new window)

16.
C. D. Sogge, Lectures on Nonlinear Wave Equations, International Press Incorporated, Boston, 1995.