Homogeneous and Non-Homogeneous Boundary Value Problems for First Order Linear Hyperbolic Systems Arising in Fluid-Mechanics. Part I.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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This report seeks to prove the existence and the uniqueness of classical and strong solutions for a class of non-homogeneous boundary value problems for first order linear hyperbolic systems arising from the dynamics of compressible non-viscous fluids. The method provides the existence of classical solutions without resorting to strong or weak solutions. A necessary and sufficient condition for the existence of solutions for the non-homogeneous problem is proved. It consists of an explicit relationship between the boundary values of u and those of the data f. Strong solutions are obtained without this supplementary assumption.
- Numerical Mathematics
- Fluid Mechanics