Well-posedness of semilinear heat equations in L1 (2019)
Journal Article

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.

A necessary and sufficient condition for uniqueness of the trivial solution in semilinear parabolic equations (2017)
Journal Article

© 2017 Elsevier Inc. In their (1968) paper Fujita and Watanabe considered the issue of uniqueness of the trivial solution of semilinear parabolic equations with respect to the class of bounded, non-negative solutions. In particular they showed that i... Read More about A necessary and sufficient condition for uniqueness of the trivial solution in semilinear parabolic equations.

A low frequency persistent reservoir of a genomic island in a pathogen population ensures island survival and improves pathogen fitness in a susceptible host (2016)
Journal Article

The co-evolution of bacterial plant pathogens and their hosts is a complex and dynamic process. Host resistance imposes stress on invading pathogens that can lead to changes in the bacterial genome enabling the pathogen to escape host resistance. We... Read More about A low frequency persistent reservoir of a genomic island in a pathogen population ensures island survival and improves pathogen fitness in a susceptible host.

A complete characterisation of local existence for semilinear heat equations in Lebesgue spaces (2015)
Journal Article

We consider the scalar semilinear heat equation ut−Δu=f(u), where f:[0,∞)→[0,∞) is continuous and non-decreasing but need not be convex. We completely characterise those functions f for which the equation has a local solution bounded in Lq(Ω) for all... Read More about A complete characterisation of local existence for semilinear heat equations in Lebesgue spaces.

Non-existence of local solutions of semilinear heat equations of Osgood type in bounded domains (2014)
Journal Article

We establish a local non-existence result for the equation ut-δu=f(u) with Dirichlet boundary conditions on a smooth bounded domain Ω⊂Rn and initial data in Lq(Ω) when the source term f is non-decreasing and limsups→∞s-γf(s)=∞ for some exponent γ>q(1... Read More about Non-existence of local solutions of semilinear heat equations of Osgood type in bounded domains.