LEADER 02621nam a2200385 i 4500 001 991003324909707536 006 m o d 007 cr cnu|||unuuu 008 170207s2014 sz a ob 001 0 eng d 020 $a9783319022727 (pbk.) 035 $ab1431616x-39ule_inst 040 $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng 082 04$a515.35$223 084 $aAMS 35L45 084 $aAMS 35L40 084 $aAMS 35L55 100 1 $aNishitani, Tatsuo$059540 245 10$aHyperbolic systems with analytic coefficients :$bwell-posedness of the Cauchy problem /$cTatsuo Nishitani 264 1$aCham :$bSpringer,$c2014 300 $aviii, 237 p. :$bill. ;$c24 cm 336 $atext$2rdacontent 337 $aunmediated$2rdamedia 338 $avolume$2rdacarrier 490 1 $aLecture notes in mathematics,$x0075-8434 ;$v2097 504 $aIncludes bibliographical references and index 505 0 $aNecessary conditions for strong hyperbolicity ; Two by two systems with two independent variables ; Systems with nondegenerate characteristics 520 $aThis monograph focuses on the well-posedness of the Cauchy problem for linear hyperbolic systems with matrix coefficients. Mainly two questions are discussed: (A) Under which conditions on lower order terms is the Cauchy problem well posed? (B) When is the Cauchy problem well posed for any lower order term? For first order two by two systems with two independent variables with real analytic coefficients, we present complete answers for both (A) and (B). For first order systems with real analytic coefficients we prove general necessary conditions for question (B) in terms of minors of the principal symbols. With regard to sufficient conditions for (B), we introduce hyperbolic systems with nondegenerate characteristics, which contains strictly hyperbolic systems, and prove that the Cauchy problem for hyperbolic systems with nondegenerate characteristics is well posed for any lower order term. We also prove that any hyperbolic system which is close to a hyperbolic system with a nondegenerate characteristic of multiple order has a nondegenerate characteristic of the same order nearby 650 0$aCauchy problem 650 0$aDifferential equations, Hyperbolic 907 $a.b1431616x$b07-02-17$c07-02-17 912 $a991003324909707536 945 $aLE013 35L NIS12 (2014)$g1$i2013000293981$lle013$op$pE44.99$q-$rl$s- $t0$u1$v0$w1$x0$y.i15795895$z07-02-17 996 $aHyperbolic systems with analytic coefficients$9820703 997 $aUNISALENTO 998 $ale013$b07-02-17$cm$da $e-$feng$gsz $h0$i0