Lower bounds for solutions of hyperbolic inequalities in unbounded regions
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- by Amy C. Murray PDF
- Proc. Amer. Math. Soc. 38 (1973), 127-134 Request permission
Abstract:
This paper considers ${C^2}$ solutions $u = u(t,x)$ of the differential inequality $|Lu| \leqq {k_1}(t,x)|u| + {k_2}(t,x)||\nabla u||$. The coefficients of the hyperbolic operator $L$ depend on both $t$ and $x$. Explicit lower bounds are given for the energy of $u$ in a region of $x$-space expanding at least as fast as wave-fronts for $L$. These bounds depend on the asymptotic behavior of ${k_1},{k_2}$, and the coefficients of $L$. They do not require boundary conditions on $u$.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 38 (1973), 127-134
- MSC: Primary 35B45; Secondary 35L10
- DOI: https://doi.org/10.1090/S0002-9939-1973-0312048-X
- MathSciNet review: 0312048