Differentiability of solutions to hyperbolic initial-boundary value problems

Authors:
Jeffrey B. Rauch and Frank J. Massey

Journal:
Trans. Amer. Math. Soc. **189** (1974), 303-318

MSC:
Primary 35L50

DOI:
https://doi.org/10.1090/S0002-9947-1974-0340832-0

MathSciNet review:
0340832

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Abstract: This paper establishes conditions for the differentiability of solutions to mixed problems for first order hyperbolic systems of the form on on . Assuming that a priori inequalities are known for this equation, it is shown that if satisfy the natural compatibility conditions associated with this equation, then the solution is of class from [0, *T*] to . These results are applied to mixed problems with distribution initial data and to quasi-linear mixed problems.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1974-0340832-0

Keywords:
A priori inequalities,
compatibility conditions,
differentiability of solutions,
distribution solutions,
generalized solutions,
hyperbolic systems,
mixed problems,
quasilinear equations

Article copyright:
© Copyright 1974
American Mathematical Society