We discuss linear autonomous evolution equations on function spaces which have the property that a positive initial value leads to a solution which initially changes sign, but then becomes – and stays – positive again for sufficiently large times. This eventual positivity phenomenon has recently been discovered for various classes of differential equations, but so far a general theory to explain this type of behaviour exists only under additional spectral assumptions.
Cite this article
Jochen Glück, Evolution equations with eventually positive solutions. Eur. Math. Soc. Mag. 123 (2022), pp. 4–11DOI 10.4171/MAG/65