On uniqueness class for a heat equation on graphs

DOI10.1016/j.jmaa.2012.04.026zbMath1246.35014OpenAlexW2035989837MaRDI QIDQ432384

Xueping Huang

Publication date: 4 July 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2012.04.026

zbMATH Keywords

graphsweighted graphstochastic completenessuniqueness class

Mathematics Subject Classification ID

Heat equation (35K05) Initial value problems for second-order parabolic equations (35K15) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (21)

Volume growth and spectrum for general graph Laplacians ⋮ Extrapolation and sampling for processes on spatial graphs ⋮ Stochastic completeness of graphs: bounded Laplacians, intrinsic metrics, volume growth and curvature ⋮ On the conservativeness and the recurrence of symmetric jump-diffusions ⋮ Ground states for logarithmic Schrödinger equations on locally finite graphs ⋮ Normalized solutions for nonlinear Schrödinger equations on graphs ⋮ Blow-up conditions for a semilinear parabolic system on locally finite graphs ⋮ Topological degree for Chern-Simons Higgs models on finite graphs ⋮ A note on the volume growth criterion for stochastic completeness of weighted graphs ⋮ A note on self-adjoint extensions of the Laplacian on weighted graphs ⋮ Self-adjoint extensions of discrete magnetic Schrödinger operators ⋮ On the uniqueness class, stochastic completeness and volume growth for graphs ⋮ Upper escape rate for weighted graphs via metric graphs ⋮ Volume growth and stochastic completeness of graphs ⋮ Escape rate of Markov chains on infinite graphs ⋮ Convergence of ground state solutions for nonlinear Schrödinger equations on graphs ⋮ Existence and convergence of solutions for nonlinear biharmonic equations on graphs ⋮ \(p\)-Laplacian equations on locally finite graphs ⋮ Time analyticity of solutions to the heat equation on graphs ⋮ Coverings and the heat equation on graphs: Stochastic incompleteness, the Feller property, and uniform transience ⋮ Stochastic Completeness of Jump Processes on Metric Measure Spaces

Cites Work

• Unnamed Item
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• Volume growth, spectrum and stochastic completeness of infinite graphs
• Gaussian upper bounds for heat kernels of continuous time simple random walks
• Stochastic incompleteness for graphs and weak Omori-Yau maximum principle
• Conservation property of symmetric jump processes
• Heat semigroup on a complete Riemannian manifold
• Analysis of the physical Laplacian and the heat flow on a locally finite graph
• On the heat kernel of a complete Riemannian manifold
• Heat kernel bounds, conservation of probability and the Feller property
• On the conservativeness and the recurrence of symmetric jump-diffusions
• Intrinsic metrics for non-local symmetric Dirichlet forms and applications to spectral theory
• The discrete integral maximum principle and its applications
• Dirichlet forms and stochastic completeness of graphs and subgraphs
• The conservation property of the heat equation on riemannian manifolds
• Behavior of diffusion semi-groups at infinity
• Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds
• Integral maximum principle and its applications
• Stochastically Incomplete Manifolds and Graphs
• Heat kernel and essential spectrum of infinite graphs
• Partial differential equations

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