A coupled non-linear hyperbolic-sobolev system |
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Authors: | Richard E Ewing |
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Institution: | (1) Rochester, Michigan, U.S.A. |
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Abstract: | Summary A boundary-initial value problem for a quasilinear hyperbolic system in one space variable is coupled to a boundary-initial
value problem for a quasilinear equation of Sobolev type in two space variables of the form Mut(x, t)+L(t) u (x, t)=f(x, t, u(x, t)) where M and L(t) are second order elliptic spacial operators. The coupling occurs through
one of the boundary conditions for the hyperbolic system and the source term in the equation of Sobolev type. Such a coupling
can arise in the consideration of oil flowing in a fissured medium and out of that medium via a pipe. Barenblatt, Zheltov,
and Kochina2] have modeled flow in a fissured medium via a special case of the above equation. A local existence and uniqueness theorem
is demonstrated. The proof involves the method of characteristics, some applications of results of R. Showalter and the contraction
mapping theorem.
Entrata in Redazione il 28 luglio 1976. |
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Keywords: | |
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