Long-time behavior of small solutions to quasilinear dissipative hyperbolic equations

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.

Asymptotic Behavior of Solutions to Quasilinear Hyperbolic Equations with Nonlinear Damping

Asymptotic behavior of solutions to dissipative Korteweg-de Vries equations

We study the large time behavior of solutions to the dissipative Korteweg-de Vries equations ut + uxxx + |D|αu + uux = 0 with 0 < α < 2. We find asymptotic expansions of the solution as t→∞ in various Sobolev norms.

Global Time Estimates for Solutions to Equations of Dissipative Type

Global time estimates of L −Lq norms of solutions to general strictly hyperbolic partial differential equations are considered. The case of special interest in this paper are equations exhibiting the dissipative behaviour. Results are applied to discuss time decay estimates for Fokker-Planck equations and for wave type equations with negative mass.

Large-time Behavior of Periodic Entropy Solutions to Anisotropic Degenerate Parabolic-hyperbolic Equations

We are interested in the large-time behavior of periodic entropy solutions in L to anisotropic degenerate parabolic-hyperbolic equations of second-order. Unlike the pure hyperbolic case, the nonlinear equation is no longer self-similar invariant and the diffusion term in the equation significantly affects the large-time behavior of solutions; thus the approach developed earlier based on the sel...