Abstract
This work develops the theory of the blow‐up phenomena for Joseph–Egri equation. The existence of the nonextendable solution of two initial‐boundary value problems (on a segment and a half‐line) is demonstrated. Sufficient conditions of the finite‐time blow‐up of these solutions, as well as the analytical estimates of the blow‐up time, are obtained. A numerical method that allows to precise the blow‐up moment for specified initial data is proposed.
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