Global classical solutions to a kind of mixed initial-boundary value problem for inhomogeneous quasilinear hyperbolic systems

In this paper, the mixed initial-boundary value problem for inhomogeneous quasilinear strictly hyperbolic systems with nonlinear boundary conditions in the first quadrant {( t, x ): t ⩾ 0, x ⩽ 0} is investigated. Under the assumption that the right-hand side satisfies a matching condition and the sy...

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Bibliographic Details
Published inApplications of mathematics (Prague) Vol. 57; no. 3; pp. 231 - 261
Main Author Yang, Yong-Fu
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.06.2012
Springer Nature B.V
Subjects
Analysis
Applications of Mathematics
Applied mathematics
Boundaries
Boundary conditions
Boundary value problems
Cauchy problems
Classical and Continuum Physics
Hyperbolic systems
Initial value problems
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical models
Mathematics
Mathematics and Statistics
Optimization
Stability
Studies
Theoretical
Uniqueness
35L50
weak linear degeneracy
mixed initial-boundary value problem
global classical solution
quasilinear hyperbolic system
matching conditon
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Summary:In this paper, the mixed initial-boundary value problem for inhomogeneous quasilinear strictly hyperbolic systems with nonlinear boundary conditions in the first quadrant {( t, x ): t ⩾ 0, x ⩽ 0} is investigated. Under the assumption that the right-hand side satisfies a matching condition and the system is strictly hyperbolic and weakly linearly degenerate, we obtain the global existence and uniqueness of a C 1 solution and its L 1 stability with certain small initial and boundary data.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0862-7940
1572-9109
DOI:10.1007/s10492-012-0015-x