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Quasilinearization Methods for Nonlinear Parabolic Equations with Functional Dependence

Published/Copyright: February 24, 2010
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Georgian Mathematical Journal
From the journal Volume 9 Issue 3

Abstract

We consider a Cauchy problem for nonlinear parabolic equations with functional dependence. We prove convergence theorems for a general quasilinearization method in two cases: (i) the Hale functional acting only on the unknown function, (ii) including partial derivatives of the unknown function.

Key words and phrases:: Parabolic; differential functional; quasilinearization; iterative method; Cauchy problem
Received: 2001-07-12
Revised: 2002-06-28
Published Online: 2010-02-24
Published in Print: 2002-September

© Heldermann Verlag

Articles in the same Issue

  1. On Appel-Type Quadrature Rules
  2. On Obtaining Dual Sequences Via Quasi-Monomiality
  3. Some Uniqueness Results for Impulsive Semilinear Neutral Functional Differential Equations
  4. Quasilinearization Methods for Nonlinear Parabolic Equations with Functional Dependence
  5. On A Generalization of the Dirichlet Integral
  6. On Ideals with Projective Bases
  7. Pseudo-Bessel Functions and Applications
  8. Holomorphic Framings for Projections in A Banach Algebra
  9. On Intersections of Small Perfect Sets
  10. On A Problem of Linear Conjugation in the Case of Nonsmooth Lines and Some Measurable Coefficients
  11. Solvability and the Unique Solvability of A Periodic Type Boundary Value Problem for First Order Scalar Functional Differential Equations
  12. On A Multiplicativity up to Homotopy of the Gugenheim Map
  13. Frame Characterizations of Besov and Triebel–Lizorkin Spaces on Spaces of Homogeneous Type and their Applications
  14. Nonexpansive Mappings and Iterative Methods in Uniformly Convex Banach Spaces
https://doi.org/10.1515/GMJ.2002.431
Keywords for this article
Parabolic; differential functional; quasilinearization; iterative method; Cauchy problem

Articles in the same Issue

  1. On Appel-Type Quadrature Rules
  2. On Obtaining Dual Sequences Via Quasi-Monomiality
  3. Some Uniqueness Results for Impulsive Semilinear Neutral Functional Differential Equations
  4. Quasilinearization Methods for Nonlinear Parabolic Equations with Functional Dependence
  5. On A Generalization of the Dirichlet Integral
  6. On Ideals with Projective Bases
  7. Pseudo-Bessel Functions and Applications
  8. Holomorphic Framings for Projections in A Banach Algebra
  9. On Intersections of Small Perfect Sets
  10. On A Problem of Linear Conjugation in the Case of Nonsmooth Lines and Some Measurable Coefficients
  11. Solvability and the Unique Solvability of A Periodic Type Boundary Value Problem for First Order Scalar Functional Differential Equations
  12. On A Multiplicativity up to Homotopy of the Gugenheim Map
  13. Frame Characterizations of Besov and Triebel–Lizorkin Spaces on Spaces of Homogeneous Type and their Applications
  14. Nonexpansive Mappings and Iterative Methods in Uniformly Convex Banach Spaces
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