5 papers · 1 filter
Strong gradient absorption and initial decay prevent blow-up
Philippe Souplet, Berikbol T. Torebek
Consider positive classical solutions of the Cauchy problem for , with sufficiently smooth initial data , in the strong absorption regime, namely $q\…
Sharp gradient bounds for uniformly elliptic PDE, eigenvalue asymptotics, and the Landis conjecture
Boyan Sirakov, Philippe Souplet
We study three classical problems in the theory of linear second-order uniformly elliptic equations: (i) gradient estimates for the Dirichlet problem, (ii) estimates and asymptotic…
Differential Harnack inequalities and maximum principles of Morel-Oswald type for elliptic PDE in divergence form
Philippe Souplet, Boyan Sirakov
This paper presents two types of novel, qualitative and quantitative, estimates for positive solutions of general uniformly elliptic PDEs in divergence form. First, we prove a More…
Blow-up for weakly superlinear heat equations and blow-up controllability of the linear heat equation
Kévin Le Balc'h, Philippe Souplet
The aim of this article is twofold: (a) to revisit the blow-up theory of weakly superlinear heat equations; (b) to explore the notion of internal global/regional blow-up controllab…
Sharp macroscopic blow-up behavior for the parabolic-elliptic Keller-Segel system in dimensions
Loth Damagui Chabi, Philippe Souplet
We study the space-time concentration or blow-up asymptotics of radially decreasing solutions of the parabolic-elliptic Keller-Segel system in the whole space or in a ball. We show…