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math.AP2025
The role of the initial distribution in population survival within a bounded habitat
Rafael de la Rosa, Elena Medina
In this paper, we analyze the role of initial conditions in population persistence. Specifically, we consider the reaction-diffusion equation $u_t\,=\,D\,(u^{ν-1}\,u_x)_x\,+\,a\,u…
math.AP2025
Lie symmetries and travelling wave solutions of the nonlinear waves in the inhomogeneous Fisher-Kolmogorov equation
M. S. Bruzón, T. M. Garrido, E. Recio +1
In this work we consider a Fisher-Kolmogorov equation depending on two exponential functions of the spatial variables. We study this equation from the point of view of symmetry red…
math.AP2024
The natural extension to PDEs of Lie's reduction of order algorithm for ODEs
George W. Bluman, Rafael de la Rosa
In this paper, we further consider the symmetry-based method for seeking nonlocally related systems for partial differential equations. In particular, we show that the symmetry-bas…