1,385 research outputs found
CONSTRUCTIVE AND INVESTIGATE THE GENERALIZED CONVOLUTION WITH THE WEIGHT FUNCTION FOR THE FOURIER COSINE AND SINE TRANSFORMS
Joint Research on Environmental Science and Technology for the Eart
RELATIONSHIP BETWEEN EROSION AND ACCUMULATION OF SEDIMENTS IN COASTAL ZONE OF BINH THUAN PROVINCE-SOUTH CENTRAL OF VIETNAM
Joint Research on Environmental Science and Technology for the Eart
Existence and Decay of Solutions of a Nonlinear Viscoelastic Problem with a Mixed Nonhomogeneous Condition
We study the initial-boundary value problem for a nonlinear wave equation
given by u_{tt}-u_{xx}+\int_{0}^{t}k(t-s)u_{xx}(s)ds+ u_{t}^{q-2}u_{t}=f(x,t,u)
, 0 < x < 1, 0 < t < T, u_{x}(0,t)=u(0,t), u_{x}(1,t)+\eta u(1,t)=g(t),
u(x,0)=\^u_{0}(x), u_{t}(x,0)={\^u}_{1}(x), where \eta \geq 0, q\geq 2 are
given constants {\^u}_{0}, {\^u}_{1}, g, k, f are given functions. In part I
under a certain local Lipschitzian condition on f, a global existence and
uniqueness theorem is proved. The proof is based on the paper [10] associated
to a contraction mapping theorem and standard arguments of density. In Part} 2,
under more restrictive conditions it is proved that the solution u(t) and its
derivative u_{x}(t) decay exponentially to 0 as t tends to infinity.Comment: 26 page
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