Long-term Behavior and Numerical Analysis of a Nonlocal Evolution Equation with Kac Potential

Autor:	Chunlei Zhang, Sarah Duffin, Jianlong Han, Seth Armstrong
Rok vydání:	2015
Předmět:	Computational Mathematics Applied Mathematics Scheme (mathematics) Bounded function Numerical analysis Evolution equation Mathematical analysis Long term behavior Limit (mathematics) Glauber Analysis Domain (mathematical analysis) Mathematics
Zdroj:	SIAM Journal on Mathematical Analysis. 47:1234-1252
ISSN:	1095-7154 0036-1410
DOI:	10.1137/130949956
Popis:	We study the long-term behavior of the solution to a nonlocal evolution equation which describes the limit of Ising spin systems with Glauber dynamics and Kac potentials on a bounded domain. We then propose an unconditionally stable, convergent finite difference scheme to this equation. We prove that the scheme is uniquely solvable, inherits the properties of the original equation, and that the numerical solution will approach the true solution in the $L^\infty$-norm.
Databáze:	OpenAIRE
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