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Article Dans Une Revue Communications in Partial Differential Equations Année : 1993

Blow-up surfaces for nonlinear wave equations, Part II

Résumé

In this second part, we prove that the equation 2u = e u has solutions blowing up near a point of any analytic, space-like hypersurface in R n , without any additional condition; if (φ(x, t) = 0) is the equation of the surface, u − ln(2/φ 2) is not necessarily analytic, and generally contains logarithmic terms. We then construct singular solutions of general semilinear equations which blow-up on a non-characteristic surface, provided that the first term of an expansion of such solutions can be found. We finally list a few other simple nonlinear evolution equations to which our methods apply; in particular, formal solutions of soliton equations given by a number of authors can be shown to be convergent by this procedure.
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Dates et versions

hal-00002669 , version 1 (12-03-2018)

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Satyanad Kichenassamy, Walter Littman. Blow-up surfaces for nonlinear wave equations, Part II. Communications in Partial Differential Equations, 1993, 18 (11), pp.1869-1899. ⟨10.1080/03605309308820997⟩. ⟨hal-00002669⟩

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