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Some remarks on my paper ”On the Cauchy problem for some non-kowalewskian equations with distinct characteristic roots. (English) Zbl 0572.35020
In our paper [ibid. 20, 105-124 (1980; Zbl 0534.35017)], we made a mistake in reasoning and proofs of Theorems 1.1 and 1.2. Prof. S. Mizohata [Proc. Japan Acad., Ser. A 57, 81-84 (1981; Zbl 0469.35039)] proposed necessary conditions and sufficient conditions for an operator given by Example 6.3 of our paper to be \(L^ 2\)-wellposed. In this paper following the inference of Mizohata, we show that for an operator with constant leading coefficients the conclusion of the Theorem 1.2 of our paper holds under the additional conditions.

MSC:
35G10 Initial value problems for linear higher-order PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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