General and optimal decay for a quasilinear viscoelastic equation

General Decay of Solutions for a Viscoelastic Equation with Balakrishnan-taylor Damping

Abstract. A viscoelastic equation with Balakrishnan-Taylor damping and nonlinear boundary/interior sources is considered in a bounded domain. Under appropriate assumptions on the relaxation function and with certain initial data and by adopting the perturbed energy method, we establish uniform decay rate of the solution energy in terms of the behavior of the relaxation function, which are not n...

A Quasilinear Viscoelastic Model for Brain Tissue

The nonlinear viscoelastic behavior of brain tissue that was observed in oscillatory shear tests was modeled with a quasilinear viscoelastic constitutive relation. The dynamic viscoelastic behavior of brain tissue has been previously modeled with only linear models. The reader is referred to Darvish (2000) for a review of the previous models. Studies on live neural tissue (Thibault et al., 1990...

The General Quasilinear Ultrahyperbolic Schrödinger Equation

 ∂tu = − i ∂xj (ajk(x, t, u, ū,∇u,∇ū)∂xku) +~b1(x, t, u, ū,∇u,∇ū) · ∇u+~b2(x, t, u, ū,∇u,∇ū) · ∇ū + c1(x, t, u, ū)u+ c2(x, t, u, ū)ū+ f(x, t), where x ∈ R, t > 0, and A = (ajk(·))j,k=1,..,n is a real, symmetric matrix. Our aim is to study the existence, uniqueness and regularity of local solutions to the initial value problem (IVP) associated to the equation (1.1). In the case where A = (ajk(·...

A Quasilinear Parabolic Equation With Inhomogeneous Density and Absorption

a benchmarking approach to optimal asset allocation for insurers and pension funds

uncertainty in the financial market will be driven by underlying brownian motions, while the assets are assumed to be general stochastic processes adapted to the filtration of the brownian motions. the goal of this study is to calculate the accumulated wealth in order to optimize the expected terminal value using a suitable utility function. this thesis introduced the lim-wong’s benchmark fun...