Geodesic
Orthogonal Solutions for a Hyperbolic System
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2008), pp. 125-130 
Ovidiu Cârjă; Mihai Necula; Ioan I. Vrabie. Orthogonal Solutions for a Hyperbolic System. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2008), pp. 125-130. http://geodesic.mathdoc.fr/item/BASM_2008_1_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the hyperbolic system $$ \begin{cases} u_t=a\nabla v+f_1(u,н)\\ v_t=a\nabla u+f_2(u,н)\\ u(0,x)=\xi(x)\\ v(0,x)=\eta(x), \end{cases} $$ and we are looking for necessary and sufficient conditions on the forcing terms $f_i$, $i=1,2$, in order that the semigroup solutions, $u$ and $н$, starting from orthogonal data $\xi,\eta\in L^2(\mathbb R^n)$, remain orthogonal on $\mathbb R_+$.

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