Abstract
In this paper we study the lifespan of solutions to nonlinear wave equations in elasticity with small initial data. Main step of our argument is to construct a good approximate solution. A natural choice of the approximation seems to be the leading term of solutions to the free elastic wave equation. However, it does not satisfy the nonlinear elastic wave equation in a suitable sense. For this reason, we modify the approximation by adding a higher-order term. Then, we are able to obtain a lower bound of the lifespan which is expressed in terms of initial data and a coefficient in the nonlinearity.
Mathematics Subject Classification. Primary 35L70; Secondary 35B40.
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Kubo, H. (2012). Lower Bounds for the Lifespan of Solutions to Nonlinear Wave Equations in Elasticity. In: Ruzhansky, M., Sugimoto, M., Wirth, J. (eds) Evolution Equations of Hyperbolic and Schrödinger Type. Progress in Mathematics, vol 301. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0454-7_10
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DOI: https://doi.org/10.1007/978-3-0348-0454-7_10
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