Quasilinear hyperbolic equations with hysteresis

Quasilinear Hyperbolic{parabolic Equations of One{dimensional Viscoelasticity

We study the global existence of solutions of initial-boundary-value problems for a quasilinear hyperbolic-parabolic equation describing the longitudinal motion of a one-dimensional viscoelastic rod. We treat a variety of nonhomogeneous boundary conditions, requiring separate analyses, because they lead to distinctive physical eeects. We employ a constitutive equation giving the stress as a gen...

A dissipative Galerkin method applied to some quasilinear hyperbolic equations

— À nonstandard continuous-in-time Galerkin method, based on piecewise polynomial spaces, is applied io the periodic initial value problem for the équation ut = a(x, ty u)ux + ƒ(*, ty «). Under the condition that a(x, t, u) > «o > 0 for the solution, optimal order L error estimâtes are derived.

Hyperbolic Trapped Rays and Global Existence of Quasilinear Wave Equations

The purpose of this paper is to give a simple proof of global existence for quadratic quasilinear Dirichlet-wave equations outside of a wide class of compact obstacles in the critical case where the spatial dimension is three. Our results improve on earlier ones in Keel, Smith and Sogge [9] in several ways. First, and most important, we can drop the star-shaped hypothesis and handle non-trappin...

Resonance for Quasilinear Hyperbolic Equation

git u) = c(8ft(ii), ? = x dt, where c(£) is a piecewise continuous function and h(u) is a smooth positive function whose first derivative does not change signs. The external effect is assumed to be finite; for simplicity, we suppose also that c(£) has compact support. Our main interest is the behavior of nonlinear waves when the resonance occurs, that is, when the characteristic speed f(u) is c...

Asymptotic Behavior of Solutions to Quasilinear Hyperbolic Equations with Nonlinear Damping