The dynamics of the fraction of never ipped spins F(t) and the average domain area A(t) of the two-dimensional, innnite-Q Potts model are investigated by zero temperature Monte Carlo simulations. It is shown that the exponents of algebraic growth of A(t) and of algebraic decay of F(t) are only eeective exponents even for very large systems and long times. Their values increase from about 0:9 fo...

From an abstract algebraic perspective, an explanation for this can be given as follows: since √ D is irrational, the polynomial t −D is irreducible over Q. Since the ring Q[t] is a PID, the irreducible element t − D generates a maximal ideal (t−D), so that the quotient Q[t]/(t−D) is a field. Moreover, the map Q[ √ D]→ Q[t]/(t −D) which is the identity on Q and sends √ D 7→ t is an isomorphism ...

In this paper, we consider a variational formulation for the Dirichlet problem of wave equation with zero boundary and initial conditions, where use integration by parts in space time. To prove unique solvability subspace H1(Q) Q being space–time domain, classical assumption is to right–hand side f L2(Q). Here, analyze generalized setting formulation, which allows us also dual test space, i.e.,...

We consider the Cauchy problem for defocusing Schrödinger (NLS) equation with a nonzero backgroundiqt+qxx−2(|q|2−1)q=0,q(x,0)=q0(x),limx→±∞⁡q0(x)=±1. Recently, space-time region |x/(2t)|<1 which is solitonic without stationary phase points on jump contour, Cuccagna and Jenkins presented asymptotic stability of N-soliton solutions NLS by using ∂¯ generalization Deift-Zhou nonlinear steepest desc...

We analyze and compute the semiclassical stress-energy flux components, outflux ${?{T}_{uu}?}_{\mathrm{ren}}$ influx ${?{T}_{vv}?}_{\mathrm{ren}}$ ($u$ $v$ being standard null Eddington coordinates), at inner horizon (IH) of a Reissner-Nordstr\"om black hole (BH) mass $M$ charge $Q$, in near-extremal domain which $Q/M$ approaches 1. consider minimally-coupled massless quantum scalar field, both...

Abstract We study the homogeneous Dirichlet problem for evolution p ( x , t )-Laplacian with nonlinear source $$\begin{aligned} u_t-{\text {div}}\left( |\nabla u|^{p(x,t)-2}\nabla u\right) =f(x,t,u),\quad (x,t)\in Q=\Omega \times (0,T). \end{aligned}$$ u t</m...

Abstract We study the existence and uniqueness of solutions of ∂tu − ∆u + u q = 0 (q > 1) in Ω×(0,∞) where Ω ⊂ R is a domain with a compact boundary, subject to the conditions u = f ≥ 0 on ∂Ω× (0,∞) and the initial condition limt→0 u(x, t) = ∞. By means of Brezis’ theory of maximal monotone operators in Hilbert spaces, we construct a minimal solution when f = 0, whatever is the regularity of th...