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Quasi-Linearisation Methods for a Non-Linear Heat Equation with Functional Dependence
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Henryk Leszczyński
Published/Copyright:
February 18, 2010
Abstract
We consider a heat equation with the non-linear right-hand side which depends on certain Volterra-type functionals acting on the unknown function and on its gradient. We give some natural sufficient conditions for the existence and uniqueness of solutions to this equation. The solution is obtained as a limit of a fast convergent sequence of successive approximations obtained by the quasi-linearisation method.
Received: 1998-09-22
Published Online: 2010-02-18
Published in Print: 2000-March
© Heldermann Verlag
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Articles in the same Issue
- On Fourier Coefficients of Functions of Generalized Wiener Class
- Asymptotic Distribution of Eigenelements of the Basic Two-Dimensional Boundary-Contact Problems of Oscillation in Classical and Couple-Stress Theories of Elasticity
- New Proofs of Two-Weight Norm Inequalities for the Maximal Operator
- Convergent Rearrangements of Series of Vector-Valued Functions
- On the Convergence and Summability of N-Dimensional Fourier Series with Respect to the Walsh–Paley Systems in the Spaces LP([0, 1]N), p ∈ [1, + ∞]
- A Direct Boundary Integral Method for a Mobility Problem
- Unconditional Convergence of Random Series and the Geometry of Banach Spaces
- Quasi-Linearisation Methods for a Non-Linear Heat Equation with Functional Dependence
- On State Space Representations of AR-Models
- On a Nonlocal Boundary Value Problem for Second Order Nonlinear Singular Differential Equations
- On the Ito formula in a Banach Space
- On the Rearranged Block-Orthonormal Systems
- Classification of Singularities at Infinity of Polynomials of Degree 4 in Two Variables
- Qualitative Investigation of Two-Dimensional Chua's System
