The eikonal equation is the nonlinear first-order partial differential equation 
, where 
is a prescribed nonnegative function. Level sets of 
describe wavefronts, and when 
is the reciprocal of a speed, 
is the travel time from an initial front. The equation is
a basic Hamilton-Jacobi equation.
Eikonal Equation
See also
Gradient, Partial Differential EquationExplore with Wolfram|Alpha
References
Evans, L. C. Partial Differential Equations, 2nd ed. Providence, RI: Amer. Math. Soc., 2010.Cite this as:
Weisstein, Eric W. "Eikonal Equation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/EikonalEquation.html