It was shown in two earlier papers that, if u(x, t) = u(x1, x2, x3, t) satisfies the wave equation in the exterior of some fixed sphere r = a and vanishes for t ⩽ r, then ru(rξ, r + τ) ∼ f(ξ, τ) as r ...

It is shown that the energy estimate is a special property of L2: similar estimates involving exponents p ≠ 2 are false. Strichartz's global Lebesgue space estimate ∥E+ f∥q ≤ C∥f∥p (E+ the forward ...

Pressure waves propagating through bubble-containing liquids in tubes experience considerable attenuation. Researchers have now derived an equation describing this phenomenon, demonstrating that ...