Solvability of Mixed Problems for the Klein–Gordon–Fock Equation in the Class Lp for p ≥ 1


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Resumo

We prove that the mixed problem for the Klein–Gordon–Fock equation utt(x, t) − uxx(x, t) + au(x, t) = 0, where a ≥ 0, in the rectangle QT = [0 ≤ x ≤ l] × [0 ≤ tT] with zero initial conditions and with the boundary conditions u(0, t) = μ(t) ∈ Lp[0, T ], u(l, t) = 0, has a unique generalized solution u(x, t) in the class Lp(QT) for p ≥ 1. We construct the solution in explicit analytic form.

Sobre autores

A. Kuleshov

Lomonosov Moscow State University; Steklov Mathematical Institute; Peoples’ Friendship University of Russia

Autor responsável pela correspondência
Email: kuleshov.a.a@yandex.ru
Rússia, Moscow, 119991; Moscow, 119991; Moscow, 117198

I. Mokrousov

Lomonosov Moscow State University; Steklov Mathematical Institute; Peoples’ Friendship University of Russia

Email: kuleshov.a.a@yandex.ru
Rússia, Moscow, 119991; Moscow, 119991; Moscow, 117198

I. Smirnov

Lomonosov Moscow State University; Steklov Mathematical Institute; Peoples’ Friendship University of Russia

Email: kuleshov.a.a@yandex.ru
Rússia, Moscow, 119991; Moscow, 119991; Moscow, 117198

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