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Instability of stationary solutions of reaction-diffusion-equations on graphs
Von Below, Joachim; Lubary Martínez, José Antonio
Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. EDP - Equacions en Derivades Parcials i Aplicacions
The nonexistence of stable stationary nonconstant solutions of reaction-diffusion-equations partial derivative(t)u(j) = partial derivative(j)(a(j)(x(j))partial derivative(j)u(j)) + f(j)(u(j)) on the edges of a finite (topological) graph is investigated under continuity and consistent Kirchhoff flow conditions at all vertices of the graph. In particular, it is shown that in the balanced autonomous case f(u) = u - u(3), no such stable stationary solution can exist on any finite graph. Finally, the balanced autonomous case is discussed on the two-sided unbounded path with equal edge lengths.
Peer Reviewed
Àrees temàtiques de la UPC::Matemàtiques i estadística
metric graphs
double-well potential
Classificació AMS::05 Combinatorics::05C Graph theory

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