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Blow-up for Semidiscretization of a Localized Semilinear Heat Equation
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D. Nabongo
Published/Copyright:
June 9, 2010
Abstract
This paper concerns the study of the numerical approximation for the following initial-boundary value problem:
where ƒ : [0, ∞) → [0, ∞) is a C2 convex, nondecreasing function,
and ε is a positive parameter. Under some assumptions, we prove that the solution of a semidiscrete form of the above problem blows up in a finite time and estimate its semidiscrete blow-up time. We also show that the semidiscrete blow-up time in certain cases converges to the real one when the mesh size tends to zero. Finally, we give some numerical experiments to illustrate our analysis.
Key words and phrases.: Semidiscretization; localized semilinear heat equation; semidiscrete blow-up time; convergence
Received: 2007-12-17
Revised: 2008-08-20
Published Online: 2010-06-09
Published in Print: 2009-December
© Heldermann Verlag
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- A New Nonlinear Lagrangian Method for Nonconvex Semidefinite Programming
- Blow-up for Semidiscretization of a Localized Semilinear Heat Equation
- Probability on Matrix-Cone Hypergroups: Limit Theorems and Structural Properties
- A System of Two Conservation Laws with Flux Conditions and Small Viscosity
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Keywords for this article
Semidiscretization;
localized semilinear heat equation;
semidiscrete blow-up time;
convergence
Articles in the same Issue
- A New Nonlinear Lagrangian Method for Nonconvex Semidefinite Programming
- Blow-up for Semidiscretization of a Localized Semilinear Heat Equation
- Probability on Matrix-Cone Hypergroups: Limit Theorems and Structural Properties
- A System of Two Conservation Laws with Flux Conditions and Small Viscosity
- Sandwich Theorems for Certain Subclasses of Analytic Functions Defined by Family of Linear Operators
- Oscillation of Solutions of Second Order Neutral Differential Equations with Positive and Negative Coefficients
