Variational principles for parabolic equations

Invariance Principles for Parabolic Equations with Random Coeecients Invariance Principles for Parabolic Equations with Random Coeecients

A general Hilbert-space-based stochastic averaging theory is brought forth in this note for arbitrary-order parabolic equations with (possibly long range dependent) random coeecients. We start with regularity conditions on the coeecients and Cauchy data of @ t u " (x; t) = X 0jkjj2p A k (x; t="; !)@ k x u " (x; t); u " (x; 0) = '(x) (1) which are only slightly stronger than those required to pr...

Variational Principles for Some Nonlinear Wave Equations

Generally speaking, there exist two basic ways to describe a physical problem [1]: (1) by differential equations (DE) with boundary or initial conditions; (2) by variational principles (VP). The VP model has many advantages over its DE partner: simple and compact in form while comprehensive in content, encompassing implicitly almost all information characterizing the problem under consideration...

Dual Variational Principles for Diffusion Equations

He's variational iteration method for fourth-order parabolic equations

He’s variational iteration method is applied to fourth-order parabolic partial differential equations with variable coefficients. To illustrate the ability and reliability of the method, some examples are given, revealing its effectiveness and simplicity. c © 2007 Published by Elsevier Ltd

A Variational Inequality for Discontinuous Solutions of Degenerate Parabolic Equations

The Beltrami framework for image processing and analysis introduces a non-linear parabolic problem, called in this context the Beltrami flow. We study in the framework for functions of bounded variation, the well-posedness of the Beltrami flow in the one-dimensional case. We prove existence and uniqueness of the weak solution using lower semi-continuity results for convex functions of measures....