Approximate solutions to second order parabolic equations. I: Analytic estimates
نویسندگان
چکیده
منابع مشابه
Approximate Solutions to Second Order Parabolic Equations I: Analytic Estimates
We establish a new type of local asymptotic formula for the Green’s function of a parabolic operator with non-constant coefficients. Our procedure leads to a construction of approximate solutions to parabolic equations which are accurate to arbitrary prescribed order in time.
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Consider positive solutions to second order elliptic equations with measurable coefficients in a bounded domain, which vanish on a portion of the boundary. We give simple necessary and sufficient geometric conditions on the domain, which guarantee the Hopf-Oleinik type estimates and the boundary Lipschitz estimates for solutions. These conditions are sharp even for harmonic functions.
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In this paper, a Chebyshev polynomial approximation for the solution of second-order partial differential equations with two variables and variable coefficients is given. Also, Chebyshev matrix is introduced. This method is based on taking the truncated Chebyshev expansions of the functions in the partial differential equations. Hence, the result matrix equation can be solved and approximate va...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2010
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.3486357