On the global solvability of the Cauchy problem for a quasilinear ultraparabolic equation

Article type: Research Article

Authors: Tersenov, Alkis S.

Affiliations: University of Crete, Department of Mathematics, 71409 Heraklion, Crete, Greece and Lavrentyev Institute of Hydrodynamics, 630090 Novosibirsk, Russia. E-mail: tersenov@math.uoc.gr

Abstract: In the present paper we study the Cauchy problem as well as the first initial boundary value problem for a class of quasilinear ultraparabolic equations. We show that the presence of the low order term satisfying a certain assumption provides a global solvability of the above problems. The optimality of this assumption is demonstrated.

Keywords: partial diffusivity, a priori estimates, global solvability

DOI: 10.3233/ASY-2012-1146

Journal: Asymptotic Analysis, vol. 82, no. 3-4, pp. 295-314, 2013