Poláčik, Peter; Yanagida, Eiji Stable subharmonic solutions of reaction-diffusion equations on an arbitrary domain. (English) Zbl 0993.35051 Discrete Contin. Dyn. Syst. 8, No. 1, 209-218 (2002). The paper is concerned with stable subharmonic solutions of the time-periodic spatially inhomogeneous reaction-diffusion equation \[ u_t=\Delta u+f(z, t, u)\qquad (x\in\Omega,\;t>0) \] where \(\Omega\) is a bounded domain in a Euclidean space and \(f\) is periodic in \(t\) with period \(\tau>0\). Besides, various boundary conditions are imposed. The authors show that stable subharmonic solutions exist on any spatial domain, provided the nonlinearity is chosen suitably. By definition, a solution \(u(x, t)\) is subharmonic if it is periodic in \(t\) with the minimal period \(k\tau\) with \(k>1\). Reviewer: Michael I.Gil’ (Beer-Sheva) Cited in 2 Documents MSC: 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations 35B10 Periodic solutions to PDEs 35K57 Reaction-diffusion equations 35B40 Asymptotic behavior of solutions to PDEs Keywords:time-periodic spatially inhomogeneous reaction-diffusion equation; monotonicity method PDFBibTeX XMLCite \textit{P. Poláčik} and \textit{E. Yanagida}, Discrete Contin. Dyn. Syst. 8, No. 1, 209--218 (2002; Zbl 0993.35051) Full Text: DOI