Abstract
We consider the Cauchy problem for systems of semilinear wave equations in two space dimensions. We present a structural condition on the nonlinearity under which the energy decreases to zero as time tends to infinity if the Cauchy data are sufficiently small, smooth and compactly-supported.
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Dedicated to Professor Shuichi Kawashima on the occasion of his sixtieth birthday
The work of S.K. is partially supported by JSPS, Grant-in-Aid for Scientific Research (C) (No. 23540241). The work of A.M. is partially supported by JSPS, Grant-in-Aid for Scientific Research (B) (No. 23340036). The work of H.S. is partially supported by JSPS, Grant-in-Aid for Scientific Research (C) (No. 25400161).
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Katayama, S., Matsumura, A. & Sunagawa, H. Energy decay for systems of semilinear wave equations with dissipative structure in two space dimensions. Nonlinear Differ. Equ. Appl. 22, 601–628 (2015). https://doi.org/10.1007/s00030-014-0297-7
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DOI: https://doi.org/10.1007/s00030-014-0297-7