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Analytical solutions for a nonlinear diffusion equation with convection and reaction

Author

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  • Valenzuela, C.
  • del Pino, L.A.
  • Curilef, S.

Abstract

Nonlinear diffusion equations with the convection and reaction terms are solved by using a power-law ansatz. This kind of equations typically appears in nonlinear problems of heat and mass transfer and flows in porous media. The solutions that we introduce in this work are analytical. At least, in the convection case, the result recovers its linear form as a special limit. In the reaction case, we define a class of nonlinearity to discuss the evolution of general solutions, we also add the Verhulst-like dynamics and global regulation. We think this method, based on this kind of ansatz, can also be applied to solve other nonlinear partial differential equations.

Suggested Citation

  • Valenzuela, C. & del Pino, L.A. & Curilef, S., 2014. "Analytical solutions for a nonlinear diffusion equation with convection and reaction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 439-451.
    • Handle: RePEc:eee:phsmap:v:416:y:2014:i:c:p:439-451
    DOI: 10.1016/j.physa.2014.08.057
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    Cited by:

    1. Atenas, Boris & Curilef, Sergio, 2021. "A statistical description for the Quasi-Stationary-States of the dipole-type Hamiltonian Mean Field Model based on a family of Vlasov solutions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 568(C).
    2. Hayek, Mohamed, 2018. "A family of analytical solutions of a nonlinear diffusion–convection equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1434-1445.

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