The Cauchy problem for a linear parabolic partial differential equation

on the goursat problem for a linear partial differential equation

in this paper, the goursat problem of a general form for a linear partial differential equation is investigated with the help of the riemann function method. some results are given concerning the existence and uniqueness for the solution of the suggested problem.

The finite element method for a linear stochastic parabolic partial differential equation driven by additive noise

Image Zooming using Non-linear Partial Differential Equation

The main issue in any image zooming techniques is to preserve the structure of the zoomed image. The zoomed image may suffer from the discontinuities in the soft regions and edges; it may contain artifacts, such as image blurring and blocky, and staircase effects. This paper presents a novel image zooming technique using Partial Differential Equations (PDEs). It combines a non-linear Fourth-ord...

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...