Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Initial-boundary value problems for the equation $ u_{tt}=(\sigma (u_x))_x+(\alpha (u_x)u_{xt})_x+f$


Authors: K. Kuttler and D. Hicks
Journal: Quart. Appl. Math. 46 (1988), 393-407
MSC: Primary 35L70; Secondary 35Q20, 73F15
DOI: https://doi.org/10.1090/qam/963578
MathSciNet review: 963578
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Abstract: Existence and uniqueness theorems are proved for global weak solutions of initial-boundary value problems corresponding to the equation

$\displaystyle {u_{tt}} = {\left( {\sigma \left( {{u_x}} \right)} \right)_x} + {\left( {\alpha \left( {{u_x}} \right){u_{xt}}} \right)_x} + f$

under assumptions that do not require smoothness or monotonicity of $ \sigma $. The initial data are not assumed to be smooth, the boundary data are allowed to be time dependent, and $ f$ is only assumed to be in $ {L^2}$.

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DOI: https://doi.org/10.1090/qam/963578
Article copyright: © Copyright 1988 American Mathematical Society


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