Mixed Cauchy problem with lateral boundary condition for noncharacteristic degenerate hyperbolic equations
Kakharman N. Kal’menov T.
December 2022Springer Science and Business Media Deutschland GmbH
Boundary Value Problems
2022#2022Issue 1
In this paper, in a cylindrical domain D= Ω × (0 , T) with Ω ⊂ Rn, we consider a mixed Cauchy problem with a potential lateral boundary condition for the following noncharacteristic degenerated equation Lu= utt− k(t) Δ xu(x, t) = f(x, t) , where k(t) ≥ 0. As in the case for strictly hyperbolic equations, we first establish that u∈W21(D) and u∈W22(D) under the assumptions ∥fk∥L2(Ω)(t)<∞ and ∥gradxfk∥L2(Ω)(t)<∞ for every t∈ [0 , T] , respectively.
Hyperbolic equation , Mixed Cauchy boundary value problem , Newton potential
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Institute of Mathematics and Mathematical Modeling, Pushkin 125, Almaty, 050010, Kazakhstan
Al-Farabi Kazakh National University, Al-Farabi 71, Almaty, 050040, Kazakhstan
Institute of Mathematics and Mathematical Modeling
Al-Farabi Kazakh National University
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