2 citations · 4 across the 5 of their papers we have counts for
5 papers
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…
Rate of convergence in the large diffusion limit for the heat equation with a dynamical boundary condition
Marek Fila, Kazuhiro Ishige, Tatsuki Kawakami +1
We study the heat equation on a half-space or on an exterior domain with a linear dynamical boundary condition. Our main aim is to establish the rate of convergence to solutions of…
Rate of Convergence to Separable Solutions of the Fast Diffusion Equation
Marek Fila, Michael Winkler
We study the asymptotic behaviour near extinction of positive solutions of the Cauchy problem for the fast diffusion equation with a subcritical exponent. We show that separable so…
A Continuum of Extinction Rates for the Fast Diffusion Equation
Marek Fila, Juan Luis Vazquez, Michael Winkler
We find a continuum of extinction rates for solutions of the fast diffusion equation in a subrange of exponents . The equation is posed in $\re…