Biharmonic heat equation with gradient non-linearity on Lp space

Gradient Estimate for the Poisson Equation and the Non-homogeneous Heat Equation on Compact Riemannian Manifolds

In this short note, we study the gradient estimate of positive solutions to Poisson equation and the non-homogeneous heat equation in a compact Riemannian manifold (Mn, g). Our results extend the gradient estimate for positive harmonic functions and positive solutions to heat equations. Mathematics Subject Classification (2000): 35J60, 53C21, 58J05

Local eventual positivity for a biharmonic heat equation in Rn∗

We study the positivity preserving property for the Cauchy problem for the linear fourth order heat equation. Although the complete positivity preserving property fails, we show that it holds eventually on compact sets.

On Univalent Solutions of the Biharmonic Equation

Remarks on non controllability of the heat equation with memory

In this paper we deal with the null controllability problem for the heat equation with a memory term by means of boundary controls. For each positive final time T and when the control is acting on the whole boundary, we prove that there exists a set of initial conditions such that the null controllability property fails.

Gradient non-linearity correction relocates normalised group activation hotspot

Introduction Gradient coils in MR scanners are assumed to produce linear magnetic field gradients, however high-speed gradients show nonlinear characteristics as a trade-off[1]. This fact creates structural deformations in MR images during reconstruction, as the gradients are assumed to be linear. A correction for these structural deformations has been shown to be imperative in multi-site struc...