scholarly journals A quasi-Newton approach to identification of a parabolic system

1998 ◽  
Vol 40 (1) ◽  
pp. 1-22 ◽  
Author(s):  
Wenhuan Yu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Parabolic System ◽  
Linear Convergence ◽  
Identification Problem ◽  
Parabolic Partial Differential Equation ◽  
Distributed Parameter ◽  
Infinite Dimensional ◽  
Nonlinear Parabolic ◽  
Quasi Newton

AbstractA quasi-Newton method (QNM) in infinite-dimensional spaces for identifying parameters involved in distributed parameter systems is presented in this paper. Next, the linear convergence of a sequence generated by the QNM algorithm is also proved. We apply the QNM algorithm to an identification problem for a nonlinear parabolic partial differential equation to illustrate the efficiency of the QNM algorithm.

scholarly journals Cauchy-Dirichlet problem for the nonlinear degenerate parabolic equations

2005 ◽  
Vol 2005 (6) ◽  
pp. 607-617 ◽  
Author(s):  
Ismail Kombe
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dirichlet Problem ◽  
Parabolic Equations ◽  
Degenerate Parabolic Equations ◽  
Parabolic Partial Differential Equation ◽  
Nonlinear Parabolic ◽  
Nonlinear Degenerate Parabolic Equations ◽  
Degenerate Parabolic ◽  
Nonlinear Degenerate

We will investigate the nonexistence of positive solutions for the following nonlinear parabolic partial differential equation:∂u/∂t=ℒu+V(w)up−1inΩ×(0,T),1<p<2,u(w,0)=u0(w)≥0inΩ,u(w,t)=0on∂Ω×(0,T)whereℒis the subellipticp-Laplacian andV∈Lloc1(Ω).

The Description of a Distributed Parameter Process through a Finite Discrete Dimensional System

2014 ◽  
Vol 657 ◽  
pp. 874-878
Author(s):  
Sever Şerban ◽  
Doina Corina Şerban
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Industrial Process ◽  
Time Discretization ◽  
Distributed Parameter ◽  
Geometrical Parameters ◽  
Dimensional System ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Distributed Parameters

This article analyses the process of warming a metal by using a walking beam furnace. This process is meant to offer the technologist objective information that may allow him to produce eventual modifications of the temperature references from the furnaces zones. Thus making the metals temperature at the furnaces exit to have an imposed distribution, within precise limits, according to the technological requests. This industrial process has a geometrical parameters distribution, more precisely it can be described through a partial differential equation, by being attached to dynamic infinite dimensional systems (or with distributed parameters). Using a procedure called geometric-time discretization (in the condition of the solutions convergence), we have managed to obtain a representation under the form of a finite discrete dimensional linear system for a process with distributed parameters.

Uniqueness of the null solution to a nonlinear partial differential equation satisfied by the explosion probability of a branching diffusion

2016 ◽  
Vol 53 (3) ◽  
pp. 938-945 ◽  
Author(s):  
K. Bruce Erickson
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Initial Conditions ◽  
Nonlinear Partial Differential Equation ◽  
Parabolic Partial Differential Equation ◽  
Partial Differential ◽  
Null Solution ◽  
Nonlinear Parabolic ◽  
Branching Diffusion ◽  
Creation Rate

AbstractThe explosion probability before time t of a branching diffusion satisfies a nonlinear parabolic partial differential equation. This equation, along with the natural boundary and initial conditions, has only the trivial solution, i.e. explosion in finite time does not occur, provided the creation rate does not grow faster than the square power at ∞.

scholarly journals A Strongly A-Stable Time Integration Method for Solving the Nonlinear Reaction-Diffusion Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Wenyuan Liao
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Time Integration ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Parabolic Partial Differential Equation ◽  
Partial Differential ◽  
Rosenbrock Method ◽  
Ode System ◽  
Nonlinear Parabolic

The semidiscrete ordinary differential equation (ODE) system resulting from compact higher-order finite difference spatial discretization of a nonlinear parabolic partial differential equation, for instance, the reaction-diffusion equation, is highly stiff. Therefore numerical time integration methods with stiff stability such as implicit Runge-Kutta methods and implicit multistep methods are required to solve the large-scale stiff ODE system. However those methods are computationally expensive, especially for nonlinear cases. Rosenbrock method is efficient since it is iteration-free; however it suffers from order reduction when it is used for nonlinear parabolic partial differential equation. In this work we construct a new fourth-order Rosenbrock method to solve the nonlinear parabolic partial differential equation supplemented with Dirichlet or Neumann boundary condition. We successfully resolved the phenomena of order reduction, so the new method is fourth-order in time when it is used for nonlinear parabolic partial differential equations. Moreover, it has been shown that the Rosenbrock method is strongly A-stable hence suitable for the stiff ODE system obtained from compact finite difference discretization of the nonlinear parabolic partial differential equation. Several numerical experiments have been conducted to demonstrate the efficiency, stability, and accuracy of the new method.

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