About the solvability behaviour for special classes of nonlinear hyperbolic equations Original Research Article

We study the question of global existence for small data solutions to the special class of semilinear wave equations View the MathML source with time-dependent coefficient in the principle part. We consider the cases of increasing and decreasing coefficients by two examples using the theory of special functions. This underlines the positive influence of increasing coefficients. Inspired by this result we prove in the last part a global existence result for small data solutions for the class of slowly oscillating coefficient functions a=a(t).