A semilinear heat equation with variable reaction and singular initial data

Carhuas-Torre B.; Castillo R.; Guzmán-Rea O.; Loayza M. · Applicable Analysis (2025) · DOI: 10.1080/00036811.2025.2489469

Resumen

We study the semilinear parabolic problem (Formula presented.) in (Formula presented.) with zero Dirichlet condition on the boundary of a smooth bounded domain (Formula presented.). We assume that (Formula presented.) is continuous satisfying (Formula presented.), (Formula presented.) is non-decreasing, and the initial data are in (Formula presented.). We prove the existence, non-existence and uniqueness of solution in the space (Formula presented.). In our approach we use the supersolution method which allows us to conclude that this solution belongs to the space (Formula presented.).

Instituciones: Universidad Tecnológica del Perú