Full paper in PDF:
$% J.-P. Dias and M. Figueira, On the existence of weak solutions for a semilinear singular hyperbolic system, Rev. Mat. Univ. Complut. Madrid 4 (1991), no. 1, 137–146.%$

On the Existence of Weak Solutions for a Semilinear Singular Hyperbolic System

João-Paulo DIAS and Mário FIGUEIRA
CMAF
2 Avd. Prof. Gama Pinto
1699 Lisboa Codex — Portugal

Received: May 23, 1990
 
ABSTRACT

In this paper we prove the existence of a weak solution for the semilinear singular real hyperbolic system

{ @u @u u--v 2 2 @@tv + @@rv +u-rv + k(u2 +v2)u= 0, r (- R+, t (- R, @t- @r + r +k(u + v )v = 0,

where k(r) is a smooth, bounded and positive function of the type n r , n >3 , in a neighborhood of zero. The initial data (u0,v0) belong to 2 2 (H (R+)) and verify

@u0 @v0 2 2 u0(0)= v0, @r (0)= - @r , (ru0,rv0) (- (L (R+)).

1980 Mathematics Subject Classification (1985 revision): 35L45, 35L60.