We study the initial-boundary value problem for a nonlinear wave equation given by utt âˆ’ uxx + âˆ« t 0 k(tâˆ’ s)uxx(s)ds+ |ut| ut = f(x, t, u), ux(0, t) = u(0, t), ux(1, t) + Î·u(1, t) = g(t), u(x, 0) = u0(x), ut(x, 0) = u1(x), where Î· â‰¥ 0, q â‰¥ 2 are given constants and u0, u1, g, k, f are given functions. In this paper, we consider two main parts. In Part 1,â€¦ (More)

During the past 10 years, the incidence of severe anaphylactic reactions during dialysis [type A first-use syndrome (FUS)] at our center has been much lower when using cuprammonium cellulose plate (CC-P) dialyzers (0/37, 750 dialyses) or coil (CC-C) dialyzers (0/32, 500) than when using cuprammonium cellulose hollow-fiber (CC-F) dialyzers (8/21,022â€¦ (More)

1 20 on the interval 0; 1] and for t 2 0; 8], we have drawn the corresponding approximate surface solution (r; t) ! u(r; t) in gure 4, obtained by successive re-initializations in t with a time step t = 1 30. Long: Linear recursive schemes associated with the non linear wave equation involving Bessel's operator. To appear in "Mathematical and Computerâ€¦ (More)

In this paper, we regularize the nonlinear inverse time heat problem in the unbounded region by Fourier method. Some new convergence rates are obtained. Meanwhile, some quite sharp error estimates between the approximate solution and exact solution are provided. Especially, the optimal convergence of the approximate solution at t = 0 is also proved. Thisâ€¦ (More)