Stable patterns for fourth-order parabolic equations
The authors study the following model equations \[ u_t=-\gamma u_{xxxx}+\beta u_{xx}- F'(u),\quad (t,x)\in\mathbb{R}^+\times (0,L), \] with \(\gamma> 0\), \(\beta> 0\). Their goal is to study stable stationary states as a function of the parameters \(\gamma\), \(\beta\), the potential \(F\), the intervallength \(L\), and the boundary conditions at \(x= 0\) and \(x\in L\). To this end they develop a new variational gluing method for constructing stable stationary states.
scientific article; zbMATH DE number 1877092