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

Abstract

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.