2 citations · 2 across the 6 of their papers we have counts for
9 papers · 1 filter
Fast diffusion equation: uniqueness of solutions with a moving singularity
Marek Fila, Petra Macková
We focus on open questions regarding the uniqueness of distributional solutions of the fast diffusion equation (FDE) with a given source term. When the source is sufficiently smoot…
Solutions with snaking singularities for the fast diffusion equation
M. Fila, J. R. King, J. Takahashi +1
We construct solutions of the fast diffusion equation, which exist for all and are singular on the set , , where $ξ\in…
The large diffusion limit for the heat equation in the exterior of the unit ball with a dynamical boundary condition
Marek Fila, Kazuhiro Ishige, Tatsuki Kawakami +1
We study the heat equation in the exterior of the unit ball with a linear dynamical boundary condition. Our main aim is to find upper and lower bounds for the rate of convergence t…
A Gagliardo-Nirenberg type inequality for rapidly decaying functions
Marek Fila, Johannes Lankeit
We improve the Gagliardo-Nirenberg inequality \[ \|φ\|_{L^q(\mathbb{R}^n)} \le C \|\nablaφ\|_{L^r(\mathbb{R}^n)} \mathcal{L}^{-(\frac 1q - \frac{n-r}{rn})} (\|\nablaφ\|_{L^r(\mathb…
Lack of smoothing for bounded solutions of a semilinear parabolic equation
Marek Fila, Johannes Lankeit
We study a semilinear parabolic equation that possesses global bounded weak solutions whose gradient has a singularity in the interior of the domain for all . The singularity…
Continuation beyond interior gradient blow-up in a semilinear parabolic equation
Marek Fila, Johannes Lankeit
It is known that there is a class of semilinear parabolic equations for which interior gradient blow-up (in finite time) occurs for some solutions. We construct a continuation of s…