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- W2080996817 abstract "We present a new method of investigating the so-called quasi-linear strongly damped wave equations $$ partial_t^2u-gammapartial_tDelta_x u-Delta_x u+f(u)= nabla_xcdot phi'(nabla_x u)+g $$ in bounded 3D domains. This method allows us to establish the existence and uniqueness of energy solutions in the case where the growth exponent of the non-linearity $phi$ is less than 6 and $f$ may have arbitrary polynomial growth rate. Moreover, the existence of a finite-dimensional global and exponential attractors for the solution semigroup associated with that equation and their additional regularity are also established. In a particular case $phiequiv0$ which corresponds to the so-called semi-linear strongly damped wave equation, our result allows to remove the long-standing growth restriction $|f(u)|leq C(1+ |u|^5)$." @default.
- W2080996817 created "2016-06-24" @default.
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- W2080996817 date "2008-07-31" @default.
- W2080996817 modified "2023-09-24" @default.
- W2080996817 title "Finite-dimensional attractors for the quasi-linear strongly-damped wave equation" @default.
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