Related Experiment Video
Updated: Aug 9, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
Lower bounds for the life-span of solutions of nonlinear wave equations in three dimensions
1Courant Institute of Mathematical Sciences, New York University, New York, New York 10012.
Abstract:
The paper deals with strict solutions u(x,t) = u(x(1),x(2),x(3),t) of an equation [Formula: see text] where Du is the set of four first derivatives of u. For given initial values u(x,0) = epsilonF(x), u(t)(x,0) = epsilonG(x), the life span T(epsilon) is defined as the supremum of all t to which the local solution can be extended for all x. Blowup in finite time corresponds to T(epsilon) < infinity. Examples show that this can occur for arbitrarily small epsilon. On the other hand, T(epsilon) must at least be very large for small epsilon. By assuming that a(ik),F,G [unk] C(infinity), that a(ik)(0) = 0, and that F,G have compact support, it is shown that [Formula: see text] for every N. This result had been established previously only for N < 4.
Related Concept Videos
Partial Differential Equations
Bessel Function of Order Zero
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Limits at Infinity
Equations of Equilibrium in Three Dimensions
According to the vector equations of equilibrium, the vector sum of all the external forces acting on a body must...
Poisson's And Laplace's Equation
