Related papers: Decay estimates for a class of wave equations
We prove descent theorems for semiorthogonal decompositions using techniques from derived algebraic geometry. Our methods allow us to capture more general filtrations of derived categories and even marked filtrations, where one descends not…
Analytical solutions of the Klein-Gordon equation are obtained by reducing the radial part of the wave equation to a standard form of a second order differential equation. Differential equations of this standard form are solvable in terms…
Qualitative properties of non-negative solutions to a quasilinear degenerate parabolic equation with an absorption term depending solely on the gradient are shown, providing information on the competition between the nonlinear diffusion and…
We address the decay rates of the energy for the damped wave equation when the damping coefficient $b$ does not satisfy the Geometric Control Condition (GCC). First, we give a link with the controllability of the associated Schr\"odinger…
Some uniform decay estimates are established for solutions of the following type of retarded integral inequalities: $$y(t)\leq E(t,\tau)||y_\tau||+\int_\tau^t K_1(t,s)||y_s||ds+\int_t^\infty K_2(t,s)||y_s||ds+\rho, \hspace{0.5cm}…
The radiative decay $B \to \phi K \gamma$ is observed for the first time. The branching fraction for the charged $B^- \to \phi K^- \gamma$ decay mode is measured to be ${\cal B}(B^- \to \phi K^- \gamma) = (3.4 \pm 0.9 \pm 0.4) \times…
The discrete Klein-Gordon equation on a two-dimensional square lattice satisfies an $\ell^1 \mapsto \ell^\infty$ dispersive bound with polynomial decay rate $|t|^{-3/4}$. We determine the shape of the light cone for any choice of the mass…
The work is devoted to Dirichlet problem for sub-quintic semi-linear wave equation with damping damping term of the form $(-\Delta)^\alpha\partial_t u$, $\alpha\in(0,\frac{1}{2})$, in bounded smooth domains of $\Bbb R^3$. It appears that to…
This pedagogical paper presents a comprehensive framework for interpreting dispersion relations across fundamental physical systems. We adopt a novel approach that starts from the mathematical form $\omega(\mathbf{k})$ and systematically…
We obtain several structure results for a class of spherical subgroups of connected reductive complex algebraic groups that extends the class of strongly solvable spherical subgroups. Based on these results, we construct certain…
Let $(\phi_t)_{t \geq 0}$ be a semigroup of holomorphic self-maps of the unit disk $\mathbb{D}$ with Denjoy-Wolff point $\tau=1$. The angular derivative is $\phi_t^{\prime}(1)= e^{-\lambda t}$, where $\lambda \geq 0$ is the spectral value…
In this paper, we first obtain the temporal decay estimates for weak solutions to the three dimensional generalized Navier-Stokes equations. Then, with these estimates at disposal, we obtain the temporal decay estimates for higher order…
We provide a uniform decay estimate of Morawetz type for the local energy of general solutions to the inhomogeneous wave equation on a Schwarzchild background. This estimate is both uniform in space and time, so in particular it implies a…
By analyzing 2.93 fb$^{-1}$ of $e^+e^-$ annihilation data taken at the center-of-mass energy $\sqrt s=$ 3.773 GeV with the BESIII detector, we determine the branching fractions of the inclusive decays $D^+\to\phi X$ and $D^0\to\phi X$ to be…
The s-wave Klein-Gordon equation for the bound states is separated in two parts to see clearly the relativistic contributions to the solution in the non-relativistic limit. The reliability of the model is discussed with the specifically…
In this paper we derive a Bismut-Elworthy formula under assumptions weaker than the non degeneracy of the noise. By Bismut-Elworthy formula we mean a gradient type estimate on the transition semigroup of a stochastic differential equation…
We give a simple proof of a pointwise decay estimate in 3+1 dimensions stated in two versions, making advantage of a particular simplicity of inverting the spherically symmetric part of the wave operator and of the comparison theorem. We…
In this paper, we prove the exponential decay of local energy for the Klein-Gordon equation with localized critical nonlinearity. The proof relies on generalized Strichartz estimates, and semi-group of Lax-Phillips.
In order to improve the frequency dispersion effects of irrotational shallow water models in coastal oceanography, several full dispersion versions of classical models were formally derived in the literature. The idea, coming from G.…
The mixing between nonstrange and strange quark wavefunctions in the $\omega$ and $\phi$ mesons leads to a small predicted branching ratio $\b(D_s^+ \to \omega e^+ \nu_e) = {\cal O}(10^{-4})(\delta/3.34^\circ)^2$, where $\delta$ is the…