Solvability of superlinear fractional parabolic equations (2022)
Journal Article
Fujishima, Y., Hisa, K., Ishige, K., & Laister, R. (2023). Solvability of superlinear fractional parabolic equations. Journal of Evolution Equations, 23(1), 4. https://doi.org/10.1007/s00028-022-00853-z

We study necessary conditions and sufficient conditions for the existence of local-in-time solutions of the Cauchy problem for superlinear fractional parabolic equations. Our conditions are sharp and clarify the relationship between the solvability o... Read More about Solvability of superlinear fractional parabolic equations.

A blow-up dichotomy for semilinear fractional heat equations (2020)
Journal Article
Laister, R., & Sierżęga, M. (2021). A blow-up dichotomy for semilinear fractional heat equations. Mathematische Annalen, 381, 75–90. https://doi.org/10.1007/s00208-020-02078-2

We derive a blow-up dichotomy for positive solutions of fractional semilinear heat equations on the whole space. That is, within a certain class of convex source terms, we establish a necessary and sufficient condition on the source for all positive... Read More about A blow-up dichotomy for semilinear fractional heat equations.

Well-posedness of semilinear heat equations in L1 (2019)
Journal Article
Laister, R., & Sierżęga, M. (2020). Well-posedness of semilinear heat equations in L1. Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 37(3), 709-725. https://doi.org/10.1016/j.anihpc.2019.12.001

The problem of obtaining necessary and sufficient conditions for local existence of non-negative solutions in Lebesgue spaces for semilinear heat equations having monotonically increasing source term f has only recently been resolved (Laister et al.... Read More about Well-posedness of semilinear heat equations in L1.