Harnessing fluctuations to discover dissipative evolution equations
نویسندگان
چکیده
منابع مشابه
Unconditional convergence of DIRK schemes applied to dissipative evolution equations
In this paper we prove the convergence of algebraically stable DIRK schemes applied to dissipative evolution equations on Hilbert spaces. The convergence analysis is unconditional as we do not impose any restrictions on the initial value or assume any extra regularity of the solution. The analysis is based on the observation that the schemes are linear combinations of the Yosida approximation, ...
متن کاملRunge-Kutta time discretizations of nonlinear dissipative evolution equations
Global error bounds are derived for Runge-Kutta time discretizations of fully nonlinear evolution equations governed by m-dissipative vector fields on Hilbert spaces. In contrast to earlier studies, the analysis presented here is not based on linearization procedures, but on the fully nonlinear framework of logarithmic Lipschitz constants in order to extend the classical B-convergence theory to...
متن کاملThe geometry of dissipative evolution equations: the porous medium equation
We show that the porous medium equation has a gradient ow structure which is both physically and mathematically natural. In order to convince the reader that it is mathematically natural, we show the time asymptotic behavior can be easily understood in this framework. We use the intuition and the calculus of Riemannian geometry to quantify this asymptotic behavior.
متن کاملNonlinear Stability for Dissipative Nonlinear Evolution Equations with Ellipticity
We study the Cauchy problem for a set of nonlinear evolution equations, which has been proposed for the investigation of nonlinear interaction between ellipticity and dissipation. The zero equilibrium is linearly stable for coeecients within certain range. We further establish the global existence, nonlinear stability and optimal decay rate of the solution for coeecients within the same range, ...
متن کاملDissipative Boussinesq equations
The classical theory of water waves is based on the theory of inviscid flows. However it is important to include viscous effects in some applications. Two models are proposed to add dissipative effects in the context of the Boussinesq equations, which include the effects of weak dispersion and nonlinearity in a shallow water framework. The dissipative Boussinesq equations are then integrated nu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the Mechanics and Physics of Solids
سال: 2019
ISSN: 0022-5096
DOI: 10.1016/j.jmps.2019.05.017