Solution Blowup for Nonlinear Equations of the Khokhlov–Zabolotskaya Type
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We consider several nonlinear evolution equations sharing a nonlinearity of the form ∂2u2/∂t2. Such a nonlinearity is present in the Khokhlov–Zabolotskaya equation, in other equations in the theory of nonlinear waves in a fluid, and also in equations in the theory of electromagnetic waves and ion–sound waves in a plasma. We consider sufficient conditions for a blowup regime to arise and find initial functions for which a solution understood in the classical sense is totally absent, even locally in time, i.e., we study the problem of an instantaneous blowup of classical solutions.
Keywordsfinite-time blowup nonlinear wave instantaneous blowup
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