Abstract
We prove that classical solutions of the dissipative wave equation $\epsilon u_{tt}+u_{t}-u_{xx}-(f(u_{x}))_{x}=0$ are globally defined in time, regardless of the size of the initial data, if $\epsilon$ is sufficiently small.
Citation
Albert Milani. "Global existence for a class of quasilinear hyperbolic-parabolic equations." Tsukuba J. Math. 19 (2) 481 - 496, December 1995. https://doi.org/10.21099/tkbjm/1496162882
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