Self-adjointness and conservation laws of difference equations
نویسندگان
چکیده
منابع مشابه
On Black-Scholes equation; method of Heir-equations, nonlinear self-adjointness and conservation laws
In this paper, Heir-equations method is applied to investigate nonclassical symmetries and new solutions of the Black-Scholes equation. Nonlinear self-adjointness is proved and infinite number of conservation laws are computed by a new conservation laws theorem.
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Each conservation law of a given partial differential equation is determined (up to equivalence) by a function known as the characteristic. This function is used to find conservation laws, to prove equivalence between conservation laws, and to prove the converse of Noether’s Theorem. Transferring these results to difference equations is nontrivial, largely because difference operators are not d...
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and Applied Analysis 3 Table 1: Nonlinear self-adjointness of (3). f g V Selfadjointness ∀(f u ̸ = 0) ∀ C 1 + C 2 eαt Nonlinear ∀(f u ̸ = 0) C 5 (C 1 + C 2 eαt)(C 3 + C 4 x) Nonlinear ∀(f u ̸ = 0) C 5 ∫f(u)du C 1 + C 2 eαt +(C 3 + C 4 e αt )e x/C5 Nonlinear C 0 ( ̸ = 0) C 1 + C 2 u C 1 e (C2/C0)x+αtu + b(t, x) Weak α is a nonzero constant; b(t, x) satisfies (27). Equation (23) can be satisfied by t...
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in this paper, heir-equations method is applied to investigate nonclassical symmetries and new solutions of the black-scholes equation. nonlinear self-adjointness is proved and infinite number of conservation laws are computed by a new conservation laws theorem.
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Some aspects of recent developments in the study of the Euler equations for compressible fluids and related hyperbolic conservation laws are analyzed and surveyed. Basic features and phenomena including convex entropy, symmetrization, hyperbolicity, genuine nonlinearity, singularities, BV bound, concentration, and cavitation are exhibited. Global well-posedness for discontinuous solutions, incl...
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ژورنال
عنوان ژورنال: Communications in Nonlinear Science and Numerical Simulation
سال: 2015
ISSN: 1007-5704
DOI: 10.1016/j.cnsns.2014.11.003