39 citations · 132 across the 10 of their papers we have counts for
10 papers
Elements represented as intersections of sets
Geir Agnarsson, Mikolaj Sierzega
For a natural number let . We say that a family is \emph{representing} if every singleton set of is an intersection of…
On the existence of global solutions for the 3D chemorepulsion system
Tomasz Cieślak, Mario Fuest, Karol Hajduk +1
In this paper, we give sufficient conditions for global-in-time existence of classical solutions for the fully parabolic chemorepulsion system posed on a convex, bounded three-dime…
A Blow-up Dichotomy for Semilinear Fractional Heat Equations
Robert Laister, Mikolaj Sierzega
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 establis…
Well-posedness of Semilinear Heat Equations in
Robert Laister, Mikolaj Sierzega
The problem of obtaining necessary and sufficient conditions for local existence of non-negative solutions in Lebesgue spaces for semilinear heat equations having monotonically inc…
A Necessary and Suffcient Condition for Uniqueness of the Trivial Solution in Semilinear Parabolic Equations
R. Laister, J. C. Robinson, M. Sierzega
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-negat…
Supersolutions for a class of nonlinear parabolic systems
Kazuhiro Ishige, Tatsuki Kawakami, Mikołaj Sierżȩga
In this paper, by using scalar nonlinear parabolic equations, we construct supersolutions for a class of nonlinear parabolic systems including $$ \left\{\begin{array}{ll} \partial_…
A complete characterisation of local existence for semilinear heat equations in Lebesgue spaces
Robert Laister, James C. Robinson, Mikolaj Sierzega +1
We consider the scalar semilinear heat equation , where is continuous and non-decreasing but need not be convex. We completely charact…
Gaussian lower bounds on the Dirichlet heat kernel and non-existence of local solutions for semilinear heat equations of Osgood type
Robert Laister, James C. Robinson, Mikolaj Sierzega
We give a simple proof of a lower bound for the Dirichlet heat kernel in terms of the Gaussian heat kernel. Using this we establish a non-existence result for semilinear heat equat…
Non-existence of local solutions for semilinear heat equations of Osgood type
Robert Laister, James C. Robinson, Mikolaj Sierzega
We establish non-existence results for the Cauchy problem of some semilinear heat equations with non-negative initial data and locally Lipschitz, nonnegative source term . Globa…
Supersolutions for a class of semilinear heat equations
James C. Robinson, Mikolaj Sierzega
A semilinear heat equation with nonnegative initial data in a subset of is considered under the assumption that is nonnegative and nondecreasing and…