42 citations · 252 across the 23 of their papers we have counts for
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Sign-indefinite second order differential operators on finite metric graphs
Amru Hussein
The question of self-adjoint realizations of sign-indefinite second order differential operators is discussed in terms of a model problem. Operators of the type $-\frac{d}{dx} \sgn…
Maximal-quasi-accretive Laplacians on finite metric graphs
Amru Hussein
For a finite not necessarily compact metric graph, one considers the differential expression on each edge. The boundary conditions at the vertices of the graph…
Bounds on the negative eigenvalues of Laplacians on finite metric graphs
Amru Hussein
For a self--adjoint Laplace operator on a finite, not necessarily compact, metric graph lower and upper bounds on each of the negative eigenvalues are derived. For compact finite m…
Quantum graphs with mixed dynamics: the transport/diffusion case
Amru Hussein, Delio Mugnolo
We introduce a class of partial differential equations on metric graphs associated with mixed evolution: on some edges we consider diffusion processes, on other ones transport phen…