MR2976045
Seiichiro WAKABAYASHI
Seiichiro WAKABAYASHI
On the Cauchy Problem for Second-Order Hyperbolic Operators with the Coefficients of Their Principal Parts Depending Only on the Time Variable
Funkcialaj Ekvacioj. Serio Internacia
55
2012
99--136
http://fe.math.kobe-u.ac.jp/FE/FullPapers/55-1/55_99.pdf
http://www.ams.org/mathscinet-getitem?mr=MR2976045
We investigate the Cauchy problem for second-order hyperbolic operators in the framework of the space of $C^\infty $ functions. In the case where the coefficients of their principal parts depend only on the time variable and are real analytic, we give a sufficient condition for $C^\infty $ well-posedness, which is also a necessary one when the space dimension is less than $3$ or the coefficients of the principal parts are semi-algebraic functions (e.g., polynomials) of the time variable.
Cauchy problem, Hyperbolic, $C^\infty$ well-posed, Second order.
Primary 35L15; Secondary 35L10.
55-99
2012
On the Cauchy Problem for Second-Order Hyperbolic Operators with the Coefficients of Their Principal Parts Depending Only on the Time Variable
Seiichiro WAKABAYASHI
Seiichiro WAKABAYASHI
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