128 citations · 387 across the 40 of their papers we have counts for
5 papers · 2 filters
Rigorous Numerical Verification of Uniqueness and Smoothness in a Surface Growth Model
Dirk Blömker, Christian Nolde, James C. Robinson
Based on numerical data and a-posteriori analysis we verify rigorously the uniqueness and smoothness of global solutions to a scalar surface growth model with striking similarities…
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…
Existence and uniqueness for a coupled parabolic-elliptic model with applications to magnetic relaxation
David S. McCormick, James C. Robinson, Jose L. Rodrigo
We prove existence, uniqueness and regularity of weak solutions of a coupled parabolic-elliptic model in two dimensions; we consider the standard equations of magnetohydrodynamics…
Generalised Gagliardo-Nirenberg inequalities using weak Lebesgue spaces and BMO
David S. McCormick, James C. Robinson, Jose L. Rodrigo
Using elementary arguments based on the Fourier transform we prove that for and with , if $f \in L^{q,\infty}(\R^n) \cap \dot{H}^…
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…