5 papers
On the closed solution of a problem coupling fluid infiltration with a hydration reaction
Diego Guevara, Sabrina Roscani, Piotr Rybka +1
We present a one-dimensional model for water infiltration coupled with a hydration reaction, relevant to coupled transport and chemical processes in the Earth's subsurface. In this…
Stabilization of solutions to a model of Langmuir-Blodgett films
Marco Morandotti, Piotr Rybka, Glen Wheeler
We show stabilisation of solutions to one-dimensional advective Cahn-Hilliard equation modeling the Langmuir-Blodgett thin films. This problem has the structure of a gradient flow…
Well-posedness and the Łojasiewicz-Simon inequality in the asymptotic analysis of a nonlinear heat equation with constraints of finite codimension
Ashish Bawalia, Zdzisław Brzeźniak, Manil T. Mohan +1
We establish the global well-posedness of the valued strong solution to a nonlinear heat equation with constraints on a \textit{Poincaré domain} $\bO\subset \R^d$ whose boun…
Asymptotic behavior of solutions to a space fractional diffusion equation
Barbara Łupińska, Piotr Rybka
We improve the time decay estimates of solutions to the one-dimensional fractional diffusion equation involving the Caputo derivative. The equation is considered on the half-line.…
Convergence of solutions of a one-phase Stefan problem with Neumann boundary data to a self-similar profile
Danielle Hilhorst, Sabrina Roscani, Piotr Rybka
We study a one-dimensional one-phase Stefan problem with a Neumann boundary condition on the fixed part of the boundary. We construct the unique self-similar solution, and show tha…