A hyperbolic free boundary problem: Existence, uniqueness and discretization. (English) Zbl 0489.35078
MSC:
35R35 | Free boundary problems for PDEs |
35L50 | Initial-boundary value problems for first-order hyperbolic systems |
35B30 | Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs |
65Z05 | Applications to the sciences |
35A05 | General existence and uniqueness theorems (PDE) (MSC2000) |
Keywords:
semidiscretization; one phase free boundary problem; existence; uniqueness; continuous dependence; method of characteristics; semidiscrete version of front trackingReferences:
[1] | Whitham G. B., Linear and nonlinear waves (1974) · Zbl 0373.76001 |
[2] | Hill C. D., J. Math. Anal. Appl. 31 pp 117– (1970) · Zbl 0203.41002 · doi:10.1016/0022-247X(70)90122-8 |
[3] | Cooke K. L., J. Math. Anal. Appl. 24 pp 372– (1968) · Zbl 0186.16902 · doi:10.1016/0022-247X(68)90038-3 |
[4] | Fasano A., ZAMM 53 pp 341– (1973) · Zbl 0257.35045 · doi:10.1002/zamm.19730530508 |
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