About the solvability behaviour for special classes of nonlinear hyperbolic equations

✍ Scribed by Jens Wirth

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 119 KB
• Volume: 52
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(02)00096-2

✦ Synopsis

We study the question of global existence for small data solutions to the special class of semilinear wave equations

with time-dependent coe cient in the principle part.

We consider the cases of increasing and decreasing coe cients by two examples using the theory of special functions. This underlines the positive in uence of increasing coe cients.

Inspired by this result we prove in the last part a global existence result for small data solutions for the class of slowly oscillating coe cient functions a = a(t).