30 citations · 86 across the 9 of their papers we have counts for
9 papers
Atmospheric Predictability Beyond 30 Days with Machine Learning
P. Trent Vonich, Gregory J. Hakim
Atmospheric predictability research has long held that rapid error growth at small spatial scales imposes an intrinsic limit of roughly two weeks on deterministic weather forecast…
Local solvability and dilation-critical singularities of supercritical fractional heat equations
Yohei Fujishima, Kotaro Hisa, Kazuhiro Ishige +1
We consider the Cauchy problem for fractional semilinear heat equations with supercritical nonlinearities and establish both necessary conditions and sufficient conditions for loca…
Solvability of Superlinear Fractional Parabolic Equations
Yohei Fujishima, Kotaro Hisa, Kazuhiro Ishige +1
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 condi…
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…
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…