59 citations · 63 across the 9 of their papers we have counts for
12 papers
On the accretivity and m-accretivity of Laplacians and porous medium-type operators on graphs
Davide Bianchi, Matthias Keller, Alberto G. Setti +1
We study the accretivity and m-accretivity of Laplacian and porous medium-type operators on weighted graphs. In particular, we give several conditions that imply these properties f…
Nonlinear parabolic characterizations of stochastic completeness at infinity on weighted graphs
Davide Bianchi, Bobo Hua, Alberto G. Setti +1
We prove a nonlinear parabolic characterization of stochastic completeness at infinity for weighted graphs. For the filtration equation \[ (\partial_t + ΔΦ)u =0 \] where is the…
The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation
Davide Bianchi, Bobo Hua, Alberto G. Setti +1
We study the Cauchy problem for the generalized porous medium equation on infinite weighted graphs. For a general nonlinearity, we establish Dirichlet comparison and weak maximum p…
The generalized porous medium equation on graphs: existence and uniqueness of solutions with data
Davide Bianchi, Alberto G. Setti, Radoslaw K. Wojciechowski
We study solutions of the generalized porous medium equation on infinite graphs. For nonnegative or nonpositive integrable data, we prove the existence and uniqueness of mild solut…
Essential self-adjointness and the -Liouville property
Bobo Hua, Jun Masamune, Radosław K. Wojciechowski
We discuss connections between the essential self-adjointness of a symmetric operator and the constancy of functions which are in the kernel of the adjoint of the operator. We then…
Stochastic completeness of graphs: bounded Laplacians, intrinsic metrics, volume growth and curvature
Radosław K. Wojciechowski
The goal of this article is to survey various results concerning stochastic completeness of graphs. In particular, we present a variety of formulations of stochastic completeness a…