Abstract
For a class of hyperbolic partial integrodifferential equations of the form $u_{tt} - u_{xx} + a*u_{xx} = 0$, fundamental solutions are found that depend on the similarity variable $\xi =x(t-|x|)^{-\alpha}$, where $\alpha \in (0,1)$ and the integral kernel $a$ behaves like $t^{-\alpha}$ near $t=0$. The asymptotic behavior of these solutions in various scaling limits and their regularity is discussed. Applications to solutions of general initial-value problems of such equations are given.
Citation
Hans Engler. "Similarity solutions for a class of hyperbolic integrodifferential equations." Differential Integral Equations 10 (5) 815 - 840, 1997. https://doi.org/10.57262/die/1367438621
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