Electronic Resource
New York, NY [u.a.]
:
Wiley-Blackwell
Numerical Methods for Partial Differential Equations
3 (1987), S. 341-355
ISSN:
0749-159X
Keywords:
Mathematics and Statistics
;
Numerical Methods
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
Notes:
We establish here the convergence (thereby proving the existence) of a semi-discrete scheme for the quasilinear hyperbolic equation where x ∊ Rn, t ∊ [0,T], and φ ∊ L∞ (Rn). It is well known that the above problem does not necessarily have global classical solutions and the usual concepts of weak solution. do not lead to a unique solution The existence of a unique solution to the above problem in a suitable sense was established in [3], where a parabolic problem obtained by introducing the term -∊Δu was studied and then the behavior as ∊ → 0 was discussed. A difference scheme approach to a problem of the above type where φi does not depend on x and t and Ψ does not depend on u was also studied in [2]. The aim of this paper is to present a proof for the case when φ depends on x, Ψ depends on u, and the technical complications in this case are nontrivial. The discussions in this paper my be considered as continuation of the ideas in the above papers.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/num.1690030406
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