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Abstract We consider the Boltzmann equation in a convex domain with a non-isothermal boundary of diffuse reflection. For both unsteady/steady problems, we construct solutions belonging to$$W^{1,p}_x$$ for any$$p<3$$ . We prove that the unsteady solution converges to the steady solution in the same Sobolev space exponentially quickly as$$t \rightarrow \infty $$ .more » « less
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