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Workshop on Messico, 2010 B. Tirozzi, S.Yu. Dobrokhotov, E. Nazaikinski “Asymptotic solutions of a 2- dimensional wave equations with degenerate velocity and localized initial conditions”
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Messico 2010 μ is a small parameter is the center of perturbation a=(1,0) Position of the Problem
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Messico 2010 Operators
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Messico 2010 Proposition
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Messico 2010 Proposition Let L be the closure of the operator L 0 Consider the differential expression a and its formal adjoint a* Let A 0 be the operator defined by a in the space D 0 and A be its closure in L 2 (R 2 + ), let A be its adjoint operator
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Messico 2010 Proposition Then the following identity holds Consider the hyperbolic problem in L 2 (R 2 + ) where L is the self-adjoint operator defined above
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Messico 2010 Proposition is a strong solution of the problem if it satisfies the equation and the initial conditions and belong to
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Messico 2010 Theorem
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Messico 2010 Asymptotic Solution of the Problem Initial Condition Lagrangian manifold Compactification of space, since p 1 goes to infinity in a finite time
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Messico 2010 Asymptotic Solution of the Problem function with compact support in Λ, regular in ρ and t, polynomial of degree N in h, fast decaying with its derivatives for ρ → ∞ Error Estimate If K h Λ [φρ(t, h)] satisfies the equation with an error of O(h N ), N > 1 the error of u is
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Messico 2010 Asymptotic Solution of the Problem
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Messico 2010 Asymptotic Solution of the Problem
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Messico 2010 Asymptotic Solution of the Problem
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Messico 2010
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Asymptotic Solution of the Problem
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Messico 2010
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