The generalized Cattaneo (telegrapher's) equation and corresponding random walks

Abstract

The various types of generalized Cattaneo, called also telegrapher's equation, are studied. We find conditions under which solutions of the equations considered so far can be recognized as probability distributions, \textit{i.e.} are normalizable and non-negative on their domains. Analysis of the relevant mean squared displacements enables us to classify diffusion processes described by such obtained solutions and to identify them with either ordinary or anomalous super- or subdiffusion. To complete our study we analyse derivations of just considered examples the generalized Cattaneo equations using the continuous time random walk and the persistent random walk approaches.

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Cited by in corpus (8)

• Stochastic dynamics with multiplicative dichotomic noise: heterogeneous telegrapher's equation, anomalous crossovers and resetting
• Integral decomposition for the solutions of the generalized Cattaneo equation
• Non-Debye relaxations: smeared time evolution, memory effects, and the Laplace exponents
• Squirrels can remember little: A random walk with jump reversals induced by a discrete-time renewal process
• Anomalous random flights and time-fractional run-and-tumble equations
• Fractional diffusion equations interpolate between damping and waves
• Operational solutions for the generalized Fokker-Planck and generalized diffusion-wave equations
• Heterogeneous Cattaneo-Vernotte equation connection to the noisy voter model