5 papers
Measure Differential Equation with a Nonlinear Growth/Decay Term
Christian Düll, Piotr Gwiazda, Anna Marciniak-Czochra +1
We obtain an existence result for a Measure Differential Equation with an additional nonlinear growth/decay term that may change the sign. The proof requires a modification of appr…
Instability of all regular stationary solutions to reaction-diffusion-ODE systems
Szymon Cygan, Anna Marciniak-Czochra, Grzegorz Karch +1
A general system of several ordinary differential equations coupled with a reaction-diffusion equation in a bounded domain with zero-flux boundary condition is studied in the conte…
Local asymptotic stability of a system of integro-differential equations describing clonal evolution of a self-renewing cell population under mutation
Jan-Erik Busse, Silvia Cuadrado, Anna Marciniak-Czochra
In this paper we consider a system of non-linear integro-differential equations (IDEs) describing evolution of a clonally heterogeneous population of malignant white blood cells (l…
A structured population model of clonal selection in acute leukemias with multiple maturation stages
Tommaso Lorenzi, Anna Marciniak-Czochra, Thomas Stiehl
Recent progress in genetic techniques has shed light on the complex co-evolution of malignant cell clones in leukemias. However, several aspects of clonal selection still remain un…
Oscillations in a white blood cell production model with multiple differentiation stages
Franziska Knauer, Thomas Stiehl, Anna Marciniak-Czochra
In this work we prove occurrence of a super-critical Hopf bifurcation in a model of white blood cell formation structured by three maturation stages. We provide an explicit analyti…