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Finite element approximation for degenerate parabolic equations. An application of nonlinear semigroup theory

Akira Mizutani, Norikazu Saito, Takashi Suzuki (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Finite element approximation for degenerate parabolic equations is considered. We propose a semidiscrete scheme provided with order-preserving and L 1 contraction properties, making use of piecewise linear trial functions and the lumping mass technique. Those properties allow us to apply nonlinear semigroup theory, and the wellposedness and stability in L 1 and L ∞ , respectively, of the scheme are established. Under certain hypotheses on the data, we also derive L 1 convergence without any convergence rate....

Finite element approximation for degenerate parabolic equations. an application of nonlinear semigroup theory

Akira Mizutani, Norikazu Saito, Takashi Suzuki (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Finite element approximation for degenerate parabolic equations is considered. We propose a semidiscrete scheme provided with order-preserving and L1 contraction properties, making use of piecewise linear trial functions and the lumping mass technique. Those properties allow us to apply nonlinear semigroup theory, and the wellposedness and stability in L1 and L∞, respectively, of the scheme are established. Under certain hypotheses on the data, we also derive L1 convergence without any...

Fixed points of Lipschitzian semigroups in Banach spaces

Jarosław Górnicki (1997)

Studia Mathematica

We prove the following theorem: Let p > 1 and let E be a real p-uniformly convex Banach space, and C a nonempty bounded closed convex subset of E. If T = T s : C → C : s ∈ G = [ 0 , ∞ ) is a Lipschitzian semigroup such that g = l i m i n f G ∋ α → ∞ i n f G ∋ δ ≥ 0 1 / α ʃ 0 α ∥ T β + δ ∥ p d β < 1 + c , where c > 0 is some constant, then there exists x ∈ C such that T s x = x for all s ∈ G.

Global Existence and Boundedness of Solutions to a Model of Chemotaxis

J. Dyson, R. Villella-Bressan, G. F. Webb (2008)

Mathematical Modelling of Natural Phenomena

A model of chemotaxis is analyzed that prevents blow-up of solutions. The model consists of a system of nonlinear partial differential equations for the spatial population density of a species and the spatial concentration of a chemoattractant in n-dimensional space. We prove the existence of solutions, which exist globally, and are L∞-bounded on finite time intervals. The hypotheses require nonlocal conditions on the species-induced production of the chemoattractant.

Gradient systems of closed operators

Vittorino Pata (2009)

Open Mathematics

A classical result on the existence of global attractors for gradient systems is extended to the case of a semigroup S(t) lacking strong continuity, but satisfying the weaker property of being a closed map for every fixed t ≥ 0.

Currently displaying 61 – 80 of 167