Initial-boundary value problems for the equation 𝑢_{𝑡𝑡}=(𝜎(𝑢ₓ))ₓ+(𝛼(𝑢ₓ)𝑢_{𝑥𝑡})ₓ+𝑓

Kuttler, K.; Hicks, D.

doi:10.1090/qam/963578

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