In this paper, we are concerned with the following fractional Schrödinger-Poisson system:    (−∆s)u + V (x)u + φu = m(x)|u|q−2|u|+ f(x,u), x ∈ Ω, (−∆t)φ = u2, x ∈ Ω, u = φ = 0, x ∈ ∂Ω, where s,t ∈ (0,1], 2t + 4s > 3, 1 < q < 2 and Ω is a bounded smooth domain of R3, and f(x,u) is linearly bounded in u at infinity. Under some assumptions on m, V and f we obtain the existence of non-trivial so...

We consider the inverse problem of determining a time-dependent potential q, appearing in the wave equation ∂2 t u−∆xu+ q(t, x)u = 0 in Q = (0, T )×Ω with Ω a C2 bounded domain of Rn, n > 2, from partial observations of the solutions on ∂Q. We prove global unique determination of a coefficient q ∈ L∞(Q).

In this paper, we consider the motion of incompressible magnetohydrodynamics (MHD) with resistivity in a domain bounded by free surface. An electromagnetic field generated some currents an external keeps MHD flow domain. On surface, boundary conditions for and transmission fields are imposed. We proved local well-posedness general setting domains from mathematical point view. The solutions obta...

In this paper, we justify the hydrostatic approximation of primitive equations in maximal $$L^p$$ - $$L^q$$ -settings three-dimensional layer domain $$\varOmega = \mathbb {T} ^2 \times (-1, 1)$$ under no-slip (Dirichlet) boundary condition any time interval (0, T) for $$T>0$$ . We show that solution to $$\epsilon $$ -scaled Navier–Stokes with Besov initial data $$u_0 \in B^{s}_{q,p}(\varOmega )...

We consider the inverse problem of determining a time-dependent damping coefficient a and a time-dependent potential q, appearing in the wave equation ∂2 t u − ∆xu + a(t, x)∂tu + q(t, x)u = 0 in Q = (0, T )×Ω, with T > 0 and Ω a C2 bounded domain of Rn, n > 2, from partial observations of the solutions on ∂Q. More precisely, we look for observations on ∂Q that allow to determine uniquely a larg...

Let u = u(q) satisfy a hyperbolic equation with impulsive input: ∂ t u(x, t)−4u(x, t) + q(x)u(x, t) = δ(x1)δ(t) and let u|t<0 = 0. Then we consider an inverse problem of determining q(x), x ∈ Ω from data u(q)|ST and (∂u(q)/∂ν) |ST . Here Ω ⊂ {(x1, . . . , xn) ∈ R|x1 > 0}, n ≥ 2, is a bounded domain, ST = {(x, t); x ∈ ∂Ω, x1 < t < T + x1}, ν = ν(x) is the unit outward normal vector to ∂Ω at x ∈ ...

We study a d-dimensional system of diffusing particles that on contact either annihilate with probability 1/(q-1) or coagulate with probability (q-2)/(q-1). In one dimension, the system models the zero-temperature Glauber dynamics of domain walls in the q-state Potts model. We calculate P(m,t), the probability that a randomly chosen lattice site contains a particle whose ancestors have undergon...

The Q-dependence of the dynamics of the fraction of never ipped spins F(t) and the average domain area A(t) of the triangular Q-state Potts model are investigated by zero temperature Monte Carlo simulations. Extending a recent study Physica A246 (1997), 519] for Q = 1 to nite Q, asymptotic values of the exponents of algebraic growth of A(t) and of algebraic decay of F(t) are determined. EEectiv...

The constraint satisfaction problem (CSP) of a first-order theory T is the computational deciding whether given conjunction atomic formulas satisfiable in some model T. We study complexity CSP$(T_1 \cup T_2)$ where $T_1$ and $T_2$ are theories with disjoint finite relational signatures. prove that if temporal structures, i.e., structures all relations have definition $(Q;<)$, then P or NP-compl...