Restrictions on the coefficients of hyperbolic systems of partial differential equations
AUTOR(ES)
John, Fritz
RESUMO
The paper deals with hyperbolic homogeneous systems [Formula: see text] of partial differential equations with constant coefficients for an N-vector u(t,x1,...,xn). 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 R81. The hyperbolic P form a closed set H in R81, the strictly hyperbolic ones an open subset Hs of H. An example is given for a P in H which is not in the closure of Hs. Moreover, it is shown that near that P the set H coincides with an algebraic manifold of codimension 4.
ACESSO AO ARTIGO
http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=431894Documentos Relacionados
- PARABOLIC SYSTEMS OF DIFFERENTIAL EQUATIONS WITH TIME-DEPENDENT COEFFICIENTS
- PARABOLIC SYSTEMS OF DIFFERENTIAL EQUATIONS WITH TIME DEPENDENT COEFFICIENTS
- REGULARITY THEOREMS FOR SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS
- RANDOM EVOLUTIONS, MARKOV CHAINS, AND SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS
- ON A NEW APPROACH TO THE COMPUTATIONAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS