Nonlinear diffusion equation, Tsallis formalism and exact solutions

DOI10.1063/1.2142838zbMath1111.82307OpenAlexW2079987131MaRDI QIDQ3438714

L. C. Malacarne, P. C. Jun. Assis, Renio S. Mendes, Luciano R. da Silva, Ervin Kaminski Lenzi

Publication date: 16 May 2007

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.2142838

Mathematics Subject Classification ID

Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Transport processes in time-dependent statistical mechanics (82C70)

Related Items (8)

Solution of the nonlinear fractional diffusion equation with absorbent term and external force ⋮ Conditional Lie-Bäcklund symmetries and sign-invariants to second-order evolution equations ⋮ An analytic algorithm for time fractional nonlinear reaction-diffusion equation based on a new iterative method ⋮ Extensions and solutions for nonlinear diffusion equations and random walks ⋮ Some results for an \({\mathcal{N}}\)-dimensional nonlinear diffusion equation with radial symmetry ⋮ A nonlinear Fokker-Planck equation approach for interacting systems: anomalous diffusion and Tsallis statistics ⋮ Conditional Lie-Bäcklund symmetries and functionally generalized separable solutions to the generalized porous medium equations with source ⋮ Nonlinear diffusion equation with reaction terms: analytical and numerical results

Cites Work

• On some diffusive waves in nonlinear heat conduction
• On some diffusive waves in a nonlinear convection-diffusion mechanism in the presence of absorption
• On some nonlinear shear flows of non-Newtonian fluids
• Anomalous diffusion coupled with Verhulst-like growth dynamics: exact time-dependent solutions
• Viscous sheets advancing over dry beds
• On a general link between anomalous diffusion and nonextensivity
• Heat waves
• Nonextensive statistical mechanics and its applications. Papers from the IMS winter school on statistical mechanics: nonextensive generalization of Boltzmann-Gibbs statistical mechanics and its applications, Okazaki, Japan, February 15--18, 1999
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