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Semilinear wave equation with time dependent potential

✍ Scribed by Nicola Visciglia

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
153 KB
Volume
27
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

We consider the following semilinear wave equation:
equation image
for (t,x) ∈ ℝ~t~ × ℝ. We prove that if the potential V(t,x) is a measurable function that satisfies the following decay assumption:
∣V(t,x)∣⩽C(1+t)(1+∣x∣) for a.e. (t,x) ∈ ℝ~t~ × ℝ
where C, σ~0~>0 are real constants, then for any real number λ that satisfies ${1+\sqrt{2}< \lambda <3}$ there exists a real number ρ(f,g,λ)>0 such that the equation has a global solution provided that 0<ρ⩽ρ(f,g,λ). Copyright © 2004 John Wiley & Sons, Ltd.

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