Abstract
There has been increasing research activity in recent years concerning the properties and the applications of nonlinear partial differential equations that are closely related to nonstandard entropic functionals, such as the Tsallis and Renyi entropies.[...]
Highlights
There has been increasing research activity in recent years concerning the properties and the applications of nonlinear partial differential equations that are closely related to nonstandard entropic functionals, such as the Tsallis and Renyi entropies
It is well known that some fundamental partial differential equations of applied mathematics and of mathematical physics—such as the linear diffusion equation—are closely linked to the standard, logarithmic Boltzmann–Gibbs–Shannon–Jaynes entropic measure
Nonlinear diffusion and Fokker–Planck equations endowed with power-law nonlinearities in the diffusion term (Laplacian term) admit exact time-dependent solutions exhibiting the form of Tsallis maximum entropy distributions, where the Tsallis measure is optimized under a small number of appropriate constraints
Summary
There has been increasing research activity in recent years concerning the properties and the applications of nonlinear partial differential equations that are closely related to nonstandard entropic functionals, such as the Tsallis and Renyi entropies. It is well known that some fundamental partial differential equations of applied mathematics and of mathematical physics—such as the linear diffusion equation—are closely linked to the standard, logarithmic Boltzmann–Gibbs–Shannon–Jaynes entropic measure. This link can be extended to the realm of nonlinear partial differential equations via the aforementioned nonstandard (or generalized) entropic functionals.
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