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Interpolation spaces and weighted pseudo almost automorphic solutions to parabolic equations and applications to fluid dynamics

Thieu Huy Nguyen, Thi Ngoc Ha Vu, The Sac Le, Truong Xuan Pham (2022)

Czechoslovak Mathematical Journal

We investigate the existence, uniqueness and polynomial stability of the weighted pseudo almost automorphic solutions to a class of linear and semilinear parabolic evolution equations. The necessary tools here are interpolation spaces and interpolation theorems which help to prove the boundedness of solution operators in appropriate spaces for linear equations. Then for the semilinear equations the fixed point arguments are used to obtain the existence and stability of the weighted pseudo almost...

Introduction to algorithms for molecular simulations

Kramář, Martin (2010)

Programs and Algorithms of Numerical Mathematics

In the first part of the paper we survey some algorithms which describe time evolution of interacting particles in a bounded domain. Applications to macroscale as well as microscale are presented on two examples: motion of planets and collision of two bodies. In the second part of the paper we present solution to stationary Schrödinger equation for simple molecular models.

Invariance of the Gibbs measure for the Benjamin–Ono equation

Yu Deng (2015)

Journal of the European Mathematical Society

In this paper we consider the periodic Benjemin-Ono equation.We establish the invariance of the Gibbs measure associated to this equation, thus answering a question raised in Tzvetkov [28]. As an intermediate step, we also obtain a local well-posedness result in Besov-type spaces rougher than L 2 , extending the L 2 well-posedness result of Molinet [20].

Invariant measures and long-time behavior for the Benjamin-Ono equation

Yu Deng, Nikolay Tzvetkov, Nicola Visciglia (2014)

Journées Équations aux dérivées partielles

We summarize the main ideas in a series of papers ([20], [21], [22], [5]) devoted to the construction of invariant measures and to the long-time behavior of solutions of the periodic Benjamin-Ono equation.

Invariant measures for the defocusing Nonlinear Schrödinger equation

Nikolay Tzvetkov (2008)

Annales de l’institut Fourier

We prove the existence and the invariance of a Gibbs measure associated to the defocusing sub-quintic Nonlinear Schrödinger equations on the disc of the plane ℝ 2 . We also prove an estimate giving some intuition to what may happen in 3 dimensions.

Invariant weighted Wiener measures and almost sure global well-posedness for the periodic derivative NLS

Andrea R. Nahmod, Tadahiro Oh, Luc Rey-Bellet, Gigliola Staffilani (2012)

Journal of the European Mathematical Society

We construct an invariant weighted Wiener measure associated to the periodic derivative nonlinear Schrödinger equation in one dimension and establish global well-posedness for data living in its support. In particular almost surely for data in a Fourier–Lebesgue space ℱ L s , r ( T ) with s ≥ 1 2 , 2 < r < 4 , ( s - 1 ) r < - 1 and scaling like H 1 2 - ϵ ( 𝕋 ) , for small ϵ > 0 . We also show the invariance of this measure.

Inverse problem for a physiologically structured population model with variable-effort harvesting

Ruslan V. Andrusyak (2017)

Open Mathematics

We consider the inverse problem of determining how the physiological structure of a harvested population evolves in time, and of finding the time-dependent effort to be expended in harvesting, so that the weighted integral of the density, which may be, for example, the total number of individuals or the total biomass, has prescribed dynamics. We give conditions for the existence of a unique, global, weak solution to the problem. Our investigation is carried out using the method of characteristics...

Investigation of the Migration/Proliferation Dichotomy and its Impact on Avascular Glioma Invasion

K. Böttger, H. Hatzikirou, A. Chauviere, A. Deutsch (2012)

Mathematical Modelling of Natural Phenomena

Gliomas are highly invasive brain tumors that exhibit high and spatially heterogeneous cell proliferation and motility rates. The interplay of proliferation and migration dynamics plays an important role in the invasion of these malignant tumors. We analyze the regulation of proliferation and migration processes with a lattice-gas cellular automaton (LGCA). We study and characterize the influence of the migration/proliferation dichotomy (also known...

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