A characteristic initial value problem for a strictly hyperbolic system

Nezam Iraniparast

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-10

Abstract:

Consider the system A u t t + C u x x = f ( x , t ) , ( x , t ) ∈ T for u ( x , t ) in ℝ 2 , where A and C are real constant 2 × 2 matrices, and f is a continuous function in ℝ 2 . We assume that det C ≠ 0 and that the system is strictly hyperbolic in the sense that there are four distinct characteristic curves Γ i , i = 1 , … , 4 , in x t -plane whose gradients ( ξ 1 i , ξ 2 i ) satisfy det [ A ξ 1 i 2 + C ξ 1 i 2 ] = 0 . We allow the characteristics of the system to be given by d t / d x = ± 1 and d t / d x = ± r , r ∈ ( 0 , 1 ) . Under special conditions on the boundaries of the region T = { ( x , t ) ≤ t ≤ 1 , ( − 1 + r + t ) / r ≤ x ≤ ( 1 + r − t ) / r } , we will show that the system has a unique C 2 solution in T .

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:375742

DOI: 10.1155/S0161171204308045

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