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Hardy uniqueness principle for the linear Schrodinger equation on quantum regular trees
Aingeru Fernández-Bertolin, Andreea Grecu, Liviu I. Ignat
In this paper we consider the linear Schrodinger equation (LSE) on a regular tree with the last generation of edges of infinite length and analyze some unique continuation properti…
Asymptotic behaviour for local and nonlocal evolution equations on metric graphs with some edges of infinite length
Liviu I. Ignat, Julio D. Rossi, Angel San Antolin
We study local (the heat equation) and nonlocal (convolution type problems with an integrable kernel) evolution problems on a metric connected finite graph in which some of the edg…
On the numerical approximations of the periodic Schrödinger equation
Liviu I. Ignat
We consider semidiscrete finite differences schemes for the periodic Scrödinger equation in dimension one. We analyze whether the space-time integrability properties observed by Bo…
From Gaussian estimates for nonlinear evolution equations to the long time behavior of branching processes
L. Beznea, L. I. Ignat, J. D. Rossi
We study solutions to the evolution equation , , in . Here the coefficients verify $ \sum_{k\geqslant 1}q_k…
Decay estimates for nonlinear nonlocal diffusion problems in the whole space
Liviu I. Ignat, Damián Pinasco, Julio D. Rossi +1
In this paper we obtain bounds for the decay rate in the $L^r (\rr^d)$-norm for the solutions to a nonlocal and nolinear evolution equation, namely, $$u_t(x,t) = \int_{\rr^d} K(x,y…
Dispersion for the Schrödinger Equation on Networks
Valeria Banica, Liviu Ignat
In this paper we consider the Schrödinger equation on a network formed by a tree with the last generation of edges formed by infinite strips. We give an explicit description of the…