| Abstract: |
| Consider the Cauchy problem for the semilinear damped wave equation
$u_{tt} - \Delta u + u_t = |u|^p$ for $t>0, x\in \mathbb{R}^n$.
By the studies conducted from the 1990s to the early 2000s, it is known that, for smooth compactly supported initial data, the critical exponent is given by the so-called Fujita critical exponent ($p=1+2/n$).
Subsequently, the critical exponent problem with non-compactly supported or slowly decaying (in general not in $L^1$) initial data has also been studied.
In this talk, we review previous studies and present some recent progress on this topic. |
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