ON INSTABILITY OF SOLUTIONS TO EVOLUTION SOBOLEV TYPE EQUATIONS ON A GRAPH

The stability and solvability of the Cauchy problem for equations $lambda u_{jt}-u_{jtxx}=eta u_{jxx}-alpha u_{jxxxx}+gamma u_j$, arised in filtering theory and defined on finit oriented connected graph with conditions of continuity and blast balance in its vertexes is under investigation.

Keywords

Sobolev type equation, graph, phase space