Restrictions on the coefficients of hyperbolic systems of partial differential equations
THE PAPER DEALS WITH HYPERBOLIC HOMOGENEOUS SYSTEMS [FORMULA: see text] of partial differential equations with constant coefficients for an N-vector u(t,x(1),...,x(n)). Here, P is a matrix form of order N and degree m. In the scalar case (N = 1), every hyperbolic P is limit of strictly hyperbolic on...
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| Vydáno v: | Proceedings of the National Academy of Sciences - PNAS Ročník 74; číslo 10; s. 4150 |
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| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
United States
01.10.1977
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| ISSN: | 0027-8424 |
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| Shrnutí: | THE PAPER DEALS WITH HYPERBOLIC HOMOGENEOUS SYSTEMS [FORMULA: see text] of partial differential equations with constant coefficients for an N-vector u(t,x(1),...,x(n)). Here, P is a matrix form of order N and degree m. In the scalar case (N = 1), every hyperbolic P is limit of strictly hyperbolic ones. This does not hold for systems as is shown here for the special case N = n = 3, m = 2. Assuming P(1,0,...,0) to be the unit matrix, we represent P by a point in R(81). The hyperbolic P form a closed set H in R(81), the strictly hyperbolic ones an open subset H(s) of H. An example is given for a P in H which is not in the closure of H(s). Moreover, it is shown that near that P the set H coincides with an algebraic manifold of codimension 4. |
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| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| ISSN: | 0027-8424 |
| DOI: | 10.1073/pnas.74.10.4150 |