A Unified Theory of Nonlinear Operator and Evolution Equations with Applications. A New Approach to Nonlinear Partial Differential Equations (Mieczyslaw Altman)

SIAM Review ◽  
1987 ◽  
Vol 29 (4) ◽  
pp. 668-670
Author(s):  
Rainer H. Picard
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Operator ◽  
Evolution Equations ◽  
Nonlinear Partial Differential Equations ◽  
Unified Theory ◽  
Partial Differential ◽  
New Approach

scholarly journals On the Bivariate Spectral Homotopy Analysis Method Approach for Solving Nonlinear Evolution Partial Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
S. S. Motsa
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Analysis Method ◽  
Partial Differential ◽  
New Approach ◽  
Homotopy Analysis ◽  
Spectral Homotopy Analysis Method

This paper presents a new application of the homotopy analysis method (HAM) for solving evolution equations described in terms of nonlinear partial differential equations (PDEs). The new approach, termed bivariate spectral homotopy analysis method (BISHAM), is based on the use of bivariate Lagrange interpolation in the so-called rule of solution expression of the HAM algorithm. The applicability of the new approach has been demonstrated by application on several examples of nonlinear evolution PDEs, namely, Fisher’s, Burgers-Fisher’s, Burger-Huxley’s, and Fitzhugh-Nagumo’s equations. Comparison with known exact results from literature has been used to confirm accuracy and effectiveness of the proposed method.

Capacity Induced by a Nonlinear Operator and Applications

2008 ◽  
Vol 15 (3) ◽  
pp. 501-516
Author(s):  
Victor A. Galaktionov ◽  
Enzo Mitidieri ◽  
Stanislav I. Pohozaev
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Operator ◽  
Blow Up ◽  
Nonlinear Partial Differential Equations ◽  
Partial Differential ◽  
Nonlinear Operators ◽  
Nonlinear Capacity ◽  
Nonlocal Nonlinearities

Abstract We consider the application of the concept of nonlinear capacity induced by nonlinear operators to blow-up problems for various types of nonlinear partial differential equations involving equations with nonlocal nonlinearities.

Sign in / Sign up

Export Citation Format

Share Document