= Spatial infinity
A <boundary condition> at <spatial infinity> specifies limiting behaviour as the spatial coordinate leaves every bounded set, such as $\lim_{x\to+\infty}u(x,t)=g(t)$ on a half-line. A pointwise limit for each time is different from uniform control over a time interval. Maximum-principle and uniqueness proofs on unbounded domains must use a suitable uniform boundedness, growth restriction or barrier hypothesis to justify passage from finite domains to infinity.
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