Geodesic
Unique solvability of pseudohyperbolic equations with singular right-hand sides
Matematičeskie zametki, Tome 80 (2006) no. 4, pp. 582-595

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In this paper, we consider the solvability of the Cauchy problem for pseudohyperbolic equations (partial differential equations of third order). For the case in which the right-hand side is a generalized function (distribution) of finite order, we establish a theorem on the unique solvability for a sufficiently general pseudohyperbolic operator. The method of proof is based on a specially constructed “scale” of a priori inequalities for the direct and adjoint operators. 
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     author = {D. A. Nomirovskii},
     title = {Unique solvability of pseudohyperbolic equations with singular right-hand sides},
     journal = {Matemati\v{c}eskie zametki},
     pages = {582--595},
     publisher = {mathdoc},
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     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_80_4_a11/}
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D. A. Nomirovskii. Unique solvability of pseudohyperbolic equations with singular right-hand sides. Matematičeskie zametki, Tome 80 (2006) no. 4, pp. 582-595. http://geodesic.mathdoc.fr/item/MZM_2006_80_4_a11/