{"product_id":"cauchy-problem-for-differential-operators-with-double-characteristics-non-effectively-hyperbolic-characteristics-von-tatsuo-nishitani","title":"Cauchy Problem for Differential Operators with Double Characteristics","description":"\n                                Combining geometrical and microlocal tools, this monograph gives detailed proofs of many well\/ill-posed results related to the Cauchy problem for differential operators with non-effectively hyperbolic double characteristics. Previously scattered over numerous different publications, the results are presented from the viewpoint that the Hamilton map and the geometry of bicharacteristics completely characterizes the well\/ill-posedness of the Cauchy problem.\n                \n                \u003cbr\u003e\n                                A doubly characteristic point of a differential operator P of order m (i.e. one where Pm = dPm = 0) is effectively hyperbolic if the Hamilton map FPm has real non-zero eigen values. When the characteristics are at most double and every double characteristic is effectively hyperbolic, the Cauchy problem for P can be solved for arbitrary lower order terms.\n                \n                \u003cbr\u003e\n                                If there is a non-effectively hyperbolic characteristic, solvability requires the subprincipal symbol of P to lie between −Pµj and Pµj, where iµj are the positive imaginary eigenvalues of FPm . Moreover, if 0 is an eigenvalue of FPm with corresponding 4 × 4 Jordan block, the spectral structure of FPm is insufficient to determine whether the Cauchy problem is well-posed and the behavior of bicharacteristics near the doubly characteristic manifold plays a crucial role.\n            \n            \u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783319676111\"\u003e\u003ch3\u003eNon-Effectively Hyperbolic Characteristics\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783319676111","offer_id":39427283484765,"sku":"9783319676111","price":53.49,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/0a41ba42-ca9f-40b4-8472-61c00d2163ec.jpg?v=1772170733","url":"https:\/\/shop.autorenwelt.de\/en\/products\/cauchy-problem-for-differential-operators-with-double-characteristics-non-effectively-hyperbolic-characteristics-von-tatsuo-nishitani","provider":"Autorenwelt Shop","version":"1.0","type":"link"}