Premium
Semilinear wave equation with time dependent potential
Author(s) -
Visciglia Nicola
Publication year - 2004
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.542
Subject(s) - mathematics , function (biology) , lambda , wave equation , mathematical analysis , mathematical physics , constant (computer programming) , combinatorics , physics , quantum mechanics , evolutionary biology , computer science , biology , programming language
We consider the following semilinear wave equation:for ( t , x ) ∈ ℝ t × ℝ x 3 . 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 ) −σ 0(1+∣ x ∣) −(2+σ 0 )for a.e. ( t , x ) ∈ ℝ t × ℝ x 3where 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.