In this paper, we consider the defocusing nonlinear wave equation $-\partial_t^ 2u+\Delta
u=| u|^{p-1} u $ in $\mathbb R\times\mathbb R^ d $. Building on our companion work …

Scattering for radial bounded solutions of focusing supercritical wave equations in odd
dimensions - ScienceDirect Skip to main contentSkip to article Elsevier logo Journals & Books …

We consider the pure-power defocusing nonlinear Klein–Gordon equation, in the H 1-
subcritical case, posed on the product space ℝ d× 𝕋, where 𝕋 is the one-dimensional flat …

We prove the existence of global solutions to the energy-supercritical wave equation in utt−
Δ u±| u| N u= 0, u (0)= u 0, ut (0)= u 1, 4< N<∞ for a large class of radially symmetric finite …

In this paper, we consider the following Cauchy problem of a weighted gradient system of
semilinear wave equations\begin {equation*}\left\{\begin {array}{lll} u_ {tt}-\Delta u=\lambda …

We establish quantitative blow-up criteria below the scaling threshold for radially symmetric
solutions to the defocusing nonlinear Schr\" odinger equation with nonlinearity $| u|^ 6u …

We establish global well-posedness and scattering results for the logarithmically energy-
supercritical nonlinear wave equation, under the assumption that the initial data satisfies a …

We carry out numerical simulations of the defocusing energy-supercritical nonlinear wave
equation for a range of spherically-symmetric initial conditions. We demonstrate numerically …

We consider the nonlinear wave equation utt− Δ u±u| u| 4 d− 1= 0 in dimensions d≥ 2. This
equation is critical in H˙ 1 2× H˙− 1 2 (R d) and subcritical with respect to the energy. We …

In this thesis, we study three problems on stochastic geometric wave equations. First, we
prove the existence of a unique local maximal solution to an energy critical stochastic wave …