Existence and characterization of characteristic points for a semilinear wave equation in one space dimension
نویسندگان
چکیده
Abstract: We consider the semilinear wave equation with power nonlinearity in one space dimension. We first show the existence of a blow-up solution with a characteristic point. Then, we consider an arbitrary blow-up solution u(x, t), the graph x 7→ T (x) of its blow-up points and S ⊂ the set of all characteristic points, and show that the S has an empty interior. Finally, given x0 ∈ S, we show that T (x) is hat shaped near x0, and that in selfsimilar variables, the solution decomposes into a decoupled sum of (at least 2) solitons (with alternate signs).
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Existence and classification of characteristic points at blow-up for a semilinear wave equation
We consider the semilinear wave equation with power nonlinearity in one space dimension. We first show the existence of a blow-up solution with a characteristic point. Then, we consider an arbitrary blow-up solution u(x, t), the graph x 7→ T (x) of its blow-up points and S ⊂ R the set of all characteristic points and show that S has an empty interior. Finally, given x0 ∈ S, we show that in self...
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