Connecting orbits in scalar reaction diffusion equations. II: The complete solution. (English) Zbl 0699.35144

Brunovský, P.; Fiedler, B.

J. Differ. Equations 81, No. 1, 106-135 (1989).

[For part I, see Dyn. Rep. 1, 57-89 (1988; Zbl 0679.35047).]
In part I the authors studied the one-dimensional reaction-diffusion equation \[ u_ t=u_{xx}+f(u),\quad x\in (0,1) \] with Dirichlet boundary conditions \(u(t,0)=u(t,1)=0\), and obtained a partial answer to the question:
(Q) Given a stationary (i.e. time-independent) solution of the above problem, which other stationary solutions does it connect to?
The present paper answers completely this question by reducing the number of exclusion principles to two.

Reviewer: J.Mawhin

MSC:

35K57

Reaction-diffusion equations

Keywords:

connection orbits; Dirichlet boundary conditions; stationary solutions; exclusion principles

Citations:

Zbl 0679.35047

References:

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