Stability diagram for a three parabolic equation system coming from Biochemistry

Bifurcation and Stability for a Nonlinear Parabolic Partial Differential Equation

This note is a brief report on some research conducted by the authors in 1971. A complete report on this same research is scheduled to appear in a separate article [2]. Let ƒ be a given function continuously mapping the real line R into itself. Let A be a given nonnegative real number. Let : [0, TT]-+R be any C^-smooth function such that (0)=<£(7r)=0. We shall be discussing the following ...

Nyquist Stability Test for a Parabolic Partial Differential Equation

The paper describes a Nyquist stability test applied to a parabolic partial differential equation. The PDE describes the temperature distribution of composite structures with linear inner heat source. The distributed transfer functions have been developed by the transmission matrix method. To analyze the stability of the system we define a virtual feedback-loop and apply the Nyquist stability t...

A three-dimensional, two-way, parabolic equation model for acoustic backscattering in a cylindrical coordinate system

A new PE model for solving three-dimensional, forward and backward sound propagation in a cylindrical coordinate system is presented. The model marches a wave field in the radial direction including the azimuthal diffraction effects, and solves for a backscattered field based on a three-dimensional, single scattering approach. A periodic sidewall boundary condition is applied for computations i...

Stability for determining the principal coefficient of parabolic equation

Optimal control and Riccati equation for a degenerate parabolic system

In this paper, we consider a stabilization problem for a fluid flow. For a perturbation of the velocity of an incoming flow on a flat plate, the laminar-to-turbulent transition location varies. We want to stabilize it by a suction velocity trough the plate. The linearization of the nonlinear model around a steady state solution leads to a linear degenerate parabolic equation. We look for a suct...