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(2009)
Solution of the Type of Running Waves for the Reaction–Nonlinear Diffusion Equation
A Friedman (1964)
Partial Differential Equations of Parabolic Type
(1964)
Translated under the title Uravneniya s chastnymi proizvodnymi parabolicheskogo tipa
(2006)
Instability of Stationary Nonmonotone Solutions of a Reaction Equation with Density-Dependent Diffusion, Differ
(1964)
Partial Differential Equations of Parabolic Type, Englewood–Cliffs
(1967)
Lineinye i kvazilineinye uravneniya parabolicheskogo tipa (Linear and Quasi-Linear Equations of Parabolic Type)
(1996)
Instability of Nonconstant Stationary Solutions of Reaction-Density-Dependent Diffusion Equations in a Convex Domain
(2005)
On the Behavior of Solutions of Parabolic Equations at Large Times
OA Ladyzhenskaya, VA Solonnikov, NN Ural’tseva (1967)
Lineinye i kvazilineinye uravneniya parabolicheskogo tipa
We consider the Cauchy problem for the reaction-nonlinear diffusion equation in a space of arbitrary dimension. On the basis of the original data of the equation, we compute the potential function, whose maximum corresponds to a dominant equilibrium distribution. For the solutions of the problem with initial distributions in a rather broad class, we prove the convergence to the dominant distribution on bounded subsets.
Differential Equations – Springer Journals
Published: May 23, 2013
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