Nonlinear Wave Equations

TL;DR: In this paper, the Korteweg de Vries equation was used for ground state construction in the context of semilinear dispersive equations and wave maps from harmonic analysis.

TL;DR: In this article, the authors show that Rademacher's theorem for functions with values in Banach spaces implies that the function m is almost everywhere differentiable on (0, T) with dm dt (t)=vt~(t, x) -m( t ) <<.

TL;DR: In this article various extensions of an old result of Fujita are considered for the initial value problem for the reaction-diffusion equation u_t =Delta u + u^p in $R^N with nonnegative initial values.

TL;DR: In this paper, the energy-critical focusing non-linear wave equation with data in the energy space, in dimensions 3, 4 and 5, was studied and it was shown that for Cauchy data of energy smaller than the one of the static solution W which gives the best constant in the Sobolev embedding, the following alternative holds.