Geodesic
Weak solutions of hyperbolic even-order operator-differential equations with variable domains
Problemy fiziki, matematiki i tehniki, no. 1 (2013), pp. 67-73

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We prove the existence and uniqueness of weak solutions $u(t)\in L_2(]0,T[,H)$ of boundary value problem for a two-term even-order hyperbolic operator-differential equation with unbounded operator coefficient $A(t)$, having $t$-depending domain $D(A(t))$. It is shown that for a smooth right-hand part the weak solutions of boundary value problem are smooth, i. e. they satisfy the equation almost everywhere on $]0,T[$ in $H$ and the boundary conditions in the usual sense. An example of the new correct boundary value problem for fourth-order partial differential equation with unsteady boundary conditions on the space variables is given.
Keywords: сorrectness by Hadamard, operator-differential equation, unbounded operator, weak solution.
Mots-clés : variable domain 
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     author = {F. E. Lomovtsev and D. A. Lyakhov},
     title = {Weak solutions of hyperbolic even-order operator-differential equations with variable domains},
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     pages = {67--73},
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     number = {1},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2013_1_a11/}
}
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F. E. Lomovtsev; D. A. Lyakhov. Weak solutions of hyperbolic even-order operator-differential equations with variable domains. Problemy fiziki, matematiki i tehniki, no. 1 (2013), pp. 67-73. http://geodesic.mathdoc.fr/item/PFMT_2013_1_a11/