Decay estimates for the linear damped wave equation on the Heisenberg group

Decay estimates of solutions to the IBq equation

‎In this paper we focus on the Cauchy problem for the generalized‎ ‎IBq equation with damped term in $n$-dimensional space‎. ‎We establish the global existence and decay estimates of solution with $L^q(1leq qleq 2)$ initial value‎, ‎provided that the initial value is suitably small‎. ‎Moreover‎, ‎we also show that the solution is asymptotic to the solution $u_L$ to the corresponding linear equa...

Achieving Arbitrarily Large Decay in the Damped Wave Equation

is referred to as the decay rate associated with a. If a is to be introduced in order to absorb an initial disturbance then one naturally wishes to strike upon that a with the least possible (most negative) decay rate. The mathematical attraction here lies in the oftnoted fact that, with respect to damping, ‘more is not better.’ More precisely, for constant a, the decay rate is not a decreasing...

Decay Estimates for the Wave Equation with Potential*

Linear dispersive decay estimates for the 3+1 dimensional water wave equation with surface tension

We consider the linearization of the three-dimensional water waves equation with surface tension about a flat interface. Using oscillatory integral methods, we prove that solutions of this equation demonstrate dispersive decay at the somewhat surprising rate of t−5/6. This rate is due to competition between surface tension and gravitation at O(1) wave numbers and is connected to the fact that, ...

on the effect of linear & non-linear texts on students comprehension and recalling

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