Natural Sciences, Mathematics, 2026
BOUNDARY VALUE PROBLEM FOR THE PSEUDOPARABOLIC EQUATIONS
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Submitted: 2025-02-27
© 2026 by author(s) and The Gufo Inc.
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Abstract
In the present paper the boundary value problem for the Sobolev type equation{∂∂tL(u(t,x))+M(u(t,x))=f(t,x),t>0, x=(x1,…,xn)∈Ω⊂Rn,u|∂Ω=0,(Lu)(0,x)=g(z),x∈Ω,
is considered, where L and M are second-order differential operators. It is proved that under some conditions this problem in the corresponding space has the unique solution.