Search results for "nonlinear evolution equation"
showing 3 items of 3 documents
An abstract doubly nonlinear equation with a measure as initial value
2007
Abstract The solvability of the abstract implicit nonlinear nonautonomous differential equation ( A ( t ) u ( t ) ) ′ + B ( t ) u ( t ) + C ( t ) u ( t ) ∋ f ( t ) will be investigated in the case of a measure as an initial value. It will be shown that this problem has a solution if the inner product of A ( t ) x and B ( t ) x + C ( t ) x is bounded below.
Decay estimates in the supremum norm for the solutions to a nonlinear evolution equation
2014
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)∣.
Nonlinear evolution equations for turbulent superfluids
2010
In this paper a system of evolution equations for turbulent superfluid helium is written in the nonlinear regime, choosing as fundamental fields the density, the velocity, the heat flux, the non-equilibrium temperature and the average vortex line density per unit volume. Approximate equations are written, where second order terms in the non-equilibrium quantities are retained.