Nonstationary Venttsel problems with discontinuous data
D.E. Apushkinskaya, A.I. Nazarov, D.K. Palagachev, L.G. Softova
TL;DR
This paper investigates Venttsel boundary value problems with discontinuous data for parabolic operators, establishing strong solvability in composite Sobolev spaces through a priori estimates.
Contribution
It provides new results on the strong solvability of nonstationary Venttsel problems with discontinuous coefficients in advanced Sobolev spaces.
Findings
Established a priori estimates for the problems.
Proved strong solvability in composite Sobolev spaces.
Extended analysis to linear and quasilinear cases.
Abstract
We study linear and quasilinear Venttsel initial-boundary value problems for parabolic operators with discontinuous coefficients. On the basis of the a priori estimates obtained, strong solvability in composite Sobolev spaces is proved.
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Taxonomy
TopicsDifferential Equations and Boundary Problems · Differential Equations and Numerical Methods · Advanced Mathematical Physics Problems