Smooth solutions of u_tt - u_xx = (u_x)^2 admit stable, explicitly written blow-up profiles with logarithmic growth, and no smooth exact self-similar blow-up exists.
Self-similar blow up for energy supercritical semilinear wave equation
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We analyse the energy supercritical semilinear wave equation $$\Phi_{tt}-\Delta\Phi-|\Phi|^{p-1}\Phi=0$$ in $\mathbb R^d$ space. We first prove in a suitable regime of parameters the existence of a countable family of self similar profiles which bifurcate from the soliton solution. We then prove the non radial finite codimensional stability of these profiles by adapting the functional setting of arXiv:1912.11005.
citation-role summary
background 1
citation-polarity summary
fields
math.AP 1years
2025 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
Blow-up of the one-dimensional wave equation with quadratic spatial derivative nonlinearity
Smooth solutions of u_tt - u_xx = (u_x)^2 admit stable, explicitly written blow-up profiles with logarithmic growth, and no smooth exact self-similar blow-up exists.