Non-existence and uniqueness results for the extended Fisher-Kolmogorov equation
We give a classification of all bounded solutions of the equation [ u'''' + p u'' + F'(u) = 0, qquad -infty < t< infty, ] in which $F$ is a general quartic polynomial and $p$ is restricted to various subsets of $(-infty,0]$. These results are obtained by combining an a priori estimate with geometric arguments in the $(u,u'')$-plane.
|Geometric quantization (msc 53D50), Geometry and quantization, symplectic methods (msc 81S10), Geometric methods in differential equations (msc 34A26), Nonlinear equations and systems, general (msc 34A34), General theory (msc 34Axx)|
|Modelling, Analysis and Simulation [MAS]|
Peletier, M.A. (1999). Non-existence and uniqueness results for the extended Fisher-Kolmogorov equation. Modelling, Analysis and Simulation [MAS]. CWI.