Publications

Publications

Papers
(2007-)

[HW08]	Hirosawa, F. and Wirth, J., C^m-theory of damped wave equations with stabilisation. J. Math. Anal. Appl. 343 (2008), no. 2, 1022-1035.
[CH08]	Cicognani, M. and Hirosawa, F., On the Gevrey well-posedness for second order strictly hyperbolic Cauchy problems under the influence of the regularity of the coefficients. Math. Scand. 102 (2008), no. 2, 283-304.
[CHR08a]	Cicognani, M., Hirosawa, F. and Reissig, M., The Log-effect for p-evolution type models. J. Math. Soc. Japan. 60 (2008), no. 3, 819-863.
[CHR08b]	Cicognani, M., Hirosawa, F. and Reissig, M., Loss of regularity for p-evolution type models. J. Math. Anal. Appl. 347 (2008), no. 1, 35-58.
[HW09]	Hirosawa, F. and Wirth, J., Generalised energy conservation law for the wave equations with variable propagation speed. J. Math. Anal. Appl. 358 (2009), no. 1, 56-74.
[H10a]	Hirosawa, F., Energy estimates for wave equations with time dependent propagation speeds in the Gevrey class. J. Differential Equations. 248 (2010), no. 12, 2972-2993.
[H10b]	Hirosawa, F., On second order weakly hyperbolic equations with oscillating coefficients and regularity loss of the solutions. Math. Nachr. 283 (2010), no. 12, 1771-1794.
[H10c]	Hirosawa, F., Energy estimates of wave equations with variable propagation speed in bounded domain. Algebraic structures in partial differential equations related to complex and Clifford analysis, 189–207, Ho Chi Ming City Univ. Educ. Press, Ho Chi Minh City, 2010.
[BuH11]	Bui T. B. N. and Hirosawa, F., On energy estimates for second order hyperbolic equations with Levi conditions for higher order regularity. Ann. Univ. Ferrara Sez. VII Sci. Mat. 57 (2011), 317-339.
[BoH1x]	Böhme, C. and Hirosawa, Generalized energy conservation for Klein-Gordon type equations. To appear in Osaka J. Math.

Preprints

[H*]	Hirosawa, F., Inooka, T. and T. D. Pham, On the global solvability for semilinear wave equations with smooth time dependent propagation speeds.

Papers
(-2006)

・ Hirosawa, F., Global solvability for the generalized degenerate Kirchhoff equation with real-analytic data in Rⁿ. Tsukuba J. Math. 21 (1997), no. 2, 483-503.

・ Hirosawa, F., Global solvability for the degenerate Kirchhoff equation. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 26 (1998), no. 1, 75-95.

・ Hirosawa, F., Energy decay for a degenerate hyperbolic equation with a dissipative term. Publ. Res. Inst. Math. Sci., Kyoto Univ. 35 (1999), no. 3, 391-406.

・ Hirosawa, F., Energy decay for degenerate hyperbolic equations of Klein-Gordon type with dissipative term. Funkcial. Ekvac. 43 (2000), no. 1, 163-191.

・ Hirosawa, F., Degenerate Kirchhoff equation in ultradifferential class. Nonlinear Anal. 48 (2002), no. 1, 77-94.

・ Hirosawa, F., On the Cauchy problem for second order strictly hyperbolic equations with non-regular coefficients. Math. Nachr. 256 (2003), 28-47.

・ Hirosawa, F., Loss of regularity for the solutions to hyperbolic equations with non-regular coefficients - an application to Kirchhoff equation -. Math. Methods Appl. Sci. 26 (2003), no. 9, 783-799.

・ Hirosawa, F. and Reissig, M., From wave to Klein-Gordon type decay rates. Nonlinear hyperbolic equations, spectral theory, and wavelet transformations, 95-155, Oper. Theory Adv. Appl., 145, Birkhäuser, Basel, 2003.

・ Hirosawa, F. and Nakazawa, H., Rapid decay of the total energy for dissipative wave equations. Tsukuba J. Math. 27 (2003), no. 2, 217-232.

・ Hirosawa, F. and Reissig, M., Well-posedness in Sobolev spaces for second order strictly hyperbolic equations with non-differentiable oscillating coefficients. Ann. Global Anal. Geom. 25 (2004), no. 2, 99-119.

・ Hirosawa, F. and Reissig, M., About the optimality of oscillations in non-Lipschitz coefficients for strictly hyperbolic equations. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) 3 (2004), no. 3, 589-608.

・ Hirosawa, F., Loss of regularity for second order hyperbolic equations with singular coefficients. Osaka J. Math. 42 (2005), no. 4, 767-790.

・ Hirosawa, F. and Reissig, M., Levi condition for hyperbolic equations with oscillating coefficients. J. Differential Equations. 223 (2006), no. 2, 329-350.

・ Hirosawa, F., Global solvability for Kirchhoff equation in special classes of non-analytic functions. J. Differential Equations. 230 (2006), no. 1, 49-70.

・ Hirosawa, F., On the asymptotic behavior of the energy for the wave equations with time depending coefficients. Math. Ann. 339 (2007), no. 4, 819-839.

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