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Łukasz Paszkowski (2012)
Applicationes Mathematicae
We investigate the two-component Nernst-Planck-Debye system by a numerical study of self-similar solutions using the Runge-Kutta method of order four and comparing the results obtained with the solutions of a one-component system. Properties of the solutions indicated by numerical simulations are proved and an existence result is established based on comparison arguments for singular ordinary differential equations.
Marek Fila, Michael Winkler (2008)
Journal of the European Mathematical Society
We consider a reaction-diffusion-convection equation on the halfline (0,1) with the zero Dirichlet boundary condition at . We find a positive selfsimilar solution which blows up in a finite time at while remains bounded for .
Sakovich, Sergei (2011)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Jan Eisner, Milan Kučera (1997)
Applications of Mathematics
We consider a reaction-diffusion system of the activator-inhibitor type with boundary conditions given by inclusions. We show that there exists a bifurcation point at which stationary but spatially nonconstant solutions (spatial patterns) bifurcate from the branch of trivial solutions. This bifurcation point lies in the domain of stability of the trivial solution to the same system with Dirichlet and Neumann boundary conditions, where a bifurcation of this classical problem is excluded.
Maria Gokieli, Nicolas Varchon (2009)
Banach Center Publications
We show existence of nonconstant stable equilibria for the Neumann reaction-diffusion problem on domains with fractures inside. We also show that the stability properties of all hyperbolic equilibria remain unchanged under domain perturbation in a quite general sense, covered by the theory of Mosco convergence.
Bonaccorsi, Stefano, Marinelli, Carlo, Ziglio, Giacomo (2008)
Electronic Journal of Probability [electronic only]
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