Abstract
where C and a are some positive constants, is uniquely solvable. Similar classes were constructed for general linear parabolic systems in [2], for semilinear second-order parabolic equations in [3], and for quasilinear higher-order parabolic equations in [4–7]; moreover, the last papers show the dependence of well-posedness classes for mixed problems in unbounded domains on geometric properties of the domains. Later, it turned out that the unique solvability of the Cauchy problem for some semilinear and nonlinear parabolic equations is independent of the behavior of the solution as |x| → +∞ [8–20]. This effect was essentially obtained for the first time in [8] for the spatially one-dimensional equation ut −∆ ( |u|p−2u ) + c|u|q−2u = 0 (1)
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