Instantaneous blow‐up versus local solvability of solutions to the Cauchy problem for the equation of a semiconductor in a magnetic fieldстатья
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Аннотация:In this paper, we consider the Cauchy problem for one nonclassical, third‐order, model partial differential equation with nonlinearity |u|^q in R^3. We show that for q ∈ (1,3], there are no local‐in‐time weak solutions of the Cauchy problem with initial functions u0(x) from a sufficiently wide class, whereas for q > 3, such a solution exists.