Radially Symmetric Wave Equations

Martin Schechter

Chapter Chapter 17 in Critical Point Theory, 2020, pp 277-291 from Springer

Abstract: Abstract In this chapter we study periodic solutions of the Dirichlet problem for the semilinear wave equation □ u : = u t t − Δ u = f ( t , x , u ) , t ∈ ℝ , x ∈ ℬ R , $$\displaystyle \square u:= u_{tt}-\Delta u = f(t,x,u),\quad t\in {\mathbb R},\quad x\in \mathcal B_R, $$ u ( t , x ) = 0 , t ∈ ℝ , x ∈ ∂ ℬ R , $$\displaystyle u(t,x) = 0,\quad t\in {\mathbb R},\quad x\in \partial \mathcal B_R, $$ u ( t + T , x ) = u ( t , x ) , t ∈ ℝ , x ∈ ℬ R , $$\displaystyle u(t+T,x) = u(t,x),\quad t\in {\mathbb R},\quad x\in \mathcal B_R, $$ where ℬ R = { x ∈ ℝ n : | x |

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-45603-0_17

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DOI: 10.1007/978-3-030-45603-0_17

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