There are a few facts that can be read off from this expression immediately. We consider t > 0 here; t < 0 is similar. First, for t0 > 0, u(x0, t0) depends on the initial data φ just at the two points x0± ct0, while it depends on the values of ψ in the whole interval [x0 − ct0, x0 + ct0]. Thus, we call the interval [x0 − ct0, x0 + ct0] the domain of dependence of (x0, t0): if the initial condit...

The final coalgebra for the finite power-set functor was described by Worrell who also proved that the final chain converges in ω + ω steps. We describe the step ω as the set of saturated trees, a concept equivalent to the modally saturated trees introduced by K. Fine in the 1970s in his study of modal logic. And for the bounded power-set functors Pλ, where λ is an infinite regular cardinal, we...

We study in detail the possibility that the flat directions of the minimal supersymmetric standard model ~MSSM! could act as a curvaton and generate the observed adiabatic density perturbations. For that the flat direction energy density has to dominate the Universe at the time when it decays. We point out that this is not possible if the inflaton decays into MSSM degrees of freedom. If the inf...

In the subcritical transition scenario, there is typically a regime where the linearly stable basic state coexists with the turbulent state. The simplest model of this is a 1D system ẏ = y(12 − y)(y − 1) where the basic state is y = 0, the ‘turbulent’ state is y = 1 and there is an intermediate state y = 12 which separates initial conditions which become turbulent (if y(0) > 12 then y(t) → 1 as...

We consider a diffusional-thermal model with twostep competitive reactions for premixed combustion wave propagation in one spatial dimension. Numerical investigation of the flame speed of the system for different fuel types shows the existence of regions where two stable travelling combustion wave solutions co-exist solutions pertaining to the fast and slow branches. A hysteresis type phenomena...

In this paper modified decomposition method is applied to the solvability of nonlinear hyperbolic equations of higher order with initial conditions and illustrated with a few simple examples. The results obtained indicate that Modified Decomposition Method is very effective and simple.

We obtain a general exact solution of the Einstein field equations for the anisotropic Bianchi type I universes filled with an exponential-potential scalar field and study their dynamics. It is shown, in agreement with previous studies, that for a wide range of initial conditions the late-time behaviour of the models is that of a power-law inflating FRW universe. This property, does not hold, i...

We consider the stochastic wave equation on the real line driven by space–time white noise and with irregular initial data. We give bounds on higher moments and, for the hyperbolic Anderson model, explicit formulas for second moments. These bounds imply weak intermittency and allow us to obtain sharp bounds on growth indices for certain classes of initial conditions with unbounded support. c ⃝ ...

We establish an analytical method leading to a more general form of the exact solution of a nonlinear ODE of the second order due to Gambier. The treatment is based on the introduction and determination of a new function, by means of which the solution of the original equation is expressed. This treatment is applied to another nonlinear equation, subjected to the same general class as that of G...

We consider continuous time random walks and discuss situations pertinent to aging. These correspond to the case when the initial state of the system is known not at preparation (at t = 0) but at the later instant of time t1 > 0 (intermediate-time initial condition). We derive the generalized aging diffusion equation for this case and express it through a single memory kernel. The results obtai...