Spectral analysis and multidimensional stability of traveling wave for nonlocal Allen-Cahn equation

Journal of Mathematical Analysis and Applications

Volumn 273, Issue 1, 2002, Pages 45-57

  Bates, Peter W ^a   Chen, Fengxin ^b  

^a BRIGHAM YOUNG UNIVERSITY   (United States)

^b UNIVERSITY OF TEXAS AT SAN ANTONIO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036756079     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-247X(02)00205-6     Document Type: Article

References (11)

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3. P.W. Bates, P.C. Fife, R.A. Gardner, C.K.R.T. Jones, The existence of traveling wave solutions of a generalized phase-field model, SIAM J. Math. Anal. 28 (1997) 60-93.
4. P.W. Bates, P.C. Fife, X. Ren, X. Wang, Traveling waves in a nonlocal model of phase transitions, Arch. Rational Mech. Anal. 138 (1997) 105-136.
5. F. Chen, Almost periodic traveling waves of nonlocal evolution equations, Nonlinear Anal., to appear.
6. I.-L. Chem, T.P. Liu, Convergence to diffusion waves of solutions for viscous conservation laws, Comm. Math. Phys. 110 (1987) 503-517.
7. X. Chen, Existence, uniqueness and asymptotic stability of traveling waves in nonlocal evolution equations, Adv. Differential Equations 2 (1997) 125-160.
8. K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, Berlin, 1985.
9. D. Henry, Geometric Theory of Semilinear Parabolic Equations, in: Lecture Notes in Math., Vol. 840, Springer-Verlag, New York, 1981.
10. C.D. Levermore, J.X. Xin, Multidimensional stability of traveling waves in a bistable reaction-diffusion equation, II, Comm. Partial Differential Equations 17 (1992) 1901-1924.
11. J.X. Xin, Multidimensional stability of traveling waves in a bistable reaction-diffusion equation, I, Comm. Partial Differential Equations 17 (1992) 1889-1899.