Homotopy of Boundary Conditions
Chapter
Abstract
Boundary conditions influence chemical reactions through diffusion and transportation of the substances, e.g. via convection and fluid flow. Diffusion is described by the Laplace operator Δ, as in the equation
for unstirred reactions. Diffusion is the underlying mechanism for spatial pattern formations. Properties and spectrum of the Laplacian are decisive for analysis of dynamics and bifurcations of reaction-diffusion equations. As we have seen in previous chapters, linear stability of a solution u= u 0 is determined by eigenvalues of the linearized operator
$$\frac{{\partial u}}{{\partial t}} = D\Delta u + f\left( {u,\lambda } \right) $$
$$D\Delta + {D_u}h\left( {{u_0},\lambda } \right). $$
Keywords
Dirichlet Problem Neumann Problem Mixed Boundary Condition Robin Boundary Condition Bifurcation Scenario
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© Springer-Verlag Berlin Heidelberg 2000