6533b856fe1ef96bd12b1e2e
RESEARCH PRODUCT
Decay estimates in the supremum norm for the solutions to a nonlinear evolution equation
Petri Juutinensubject
Uniform normGeneral MathematicsMathematical analysista111CylinderViscosity solutionNonlinear evolutionStationary solutionnonlinear evolution equationBoundary valuesMathematicsdescription
We study the asymptotic behaviour, as t → ∞, of the solutions to the nonlinear evolution equationwhere ΔpNu = Δu + (p−2) (D2u(Du/∣Du∣)) · (Du/∣Du∣) is the normalized p-Laplace equation and p ≥ 2. We show that if u(x,t) is a viscosity solution to the above equation in a cylinder Ω × (0, ∞) with time-independent lateral boundary values, then it converges to the unique stationary solution h as t → ∞. Moreover, we provide an estimate for the decay rate of maxx∈Ω∣u(x,t) − h(x)∣.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-05-16 | Proceedings of the Royal Society of Edinburgh, Section: A Mathematics |