{"product_id":"9783319676111","title":"Cauchy Problem for Differential Operators with Double Characteristics","description":"Combining geometrical and microlocal tools, this monograph gives detailed proofs of many well\/ill-posed results related to the Cauchy problem for di?erential operators with non-e?ectively hyperbolic double characteristics. Previously scattered over numerous di?erent 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.\u003cdiv\u003e\u003c\/div\u003e\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e\u003cdiv\u003eA doubly characteristic point of a di?erential operator P of order m (i.e. one where Pm = dPm = 0) is e?ectively hyperbolic if the Hamilton map FPm has real non-zero eigen values. When the characteristics are at most double and every double characteristic is e?ectively hyperbolic, the Cauchy problem for P can be solved for arbitrary lower order terms.\u003c\/div\u003e\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e\u003cdiv\u003eIf there is a non-e?ectively 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 insu?cient to determine whether the Cauchy problem is well-posed and the behavior of bicharacteristics near the doubly characteristic manifold plays a crucial role.\u003c\/div\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003ePublication Year: \u003c\/strong\u003e2017\u003cbr\u003e\u003cstrong\u003eImprint: \u003c\/strong\u003eSpringer International Publishing\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003eFormat: P\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003eWeight (Gram): 349\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003c\/p\u003e","brand":"Tatsuo Nishitani","offers":[{"title":"Default Title","offer_id":41241828819122,"sku":"9783319676111","price":1106665.0,"currency_code":"IDR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0502\/5382\/4178\/products\/3319676113.01_SCLZZZZZZZ.jpg?v=1635515773","url":"https:\/\/readabook.store\/en-id\/products\/9783319676111","provider":"READABOOK BY ALKEM","version":"1.0","type":"link"}