Displaying similar documents to “Local existence for a general model of size-dependent population dynamics.”

The Rothe method for the McKendrick-von Foerster equation

Henryk Leszczyński, Piotr Zwierkowski (2013)

Czechoslovak Mathematical Journal

Similarity:

We present the Rothe method for the McKendrick-von Foerster equation with initial and boundary conditions. This method is well known as an abstract Euler scheme in extensive literature, e.g. K. Rektorys, The Method of Discretization in Time and Partial Differential Equations, Reidel, Dordrecht, 1982. Various Banach spaces are exploited, the most popular being the space of bounded and continuous functions. We prove the boundedness of approximate solutions and stability of the Rothe method...

The long-time behaviour of the solutions to semilinear stochastic partial differential equations on the whole space

Ralf Manthey (2001)

Mathematica Bohemica

Similarity:

The Cauchy problem for a stochastic partial differential equation with a spatial correlated Gaussian noise is considered. The "drift" is continuous, one-sided linearily bounded and of at most polynomial growth while the "diffusion" is globally Lipschitz continuous. In the paper statements on existence and uniqueness of solutions, their pathwise spatial growth and on their ultimate boundedness as well as on asymptotical exponential stability in mean square in a certain Hilbert space of...