Integral Representations for the Barenblatt–Sobolev–Galpern Pseudo-Parabolic Equation: Boundary-Value and Interface Problems on Unbounded and Finite Intervals
Chatziafratis A, Rukolaine SA, Aifantis EC (2026)
Publication Type: Journal article
Publication year: 2026
Journal
Book Volume: 33
Pages Range: 465-491
Journal Issue: 3
DOI: 10.1134/S1061920825601739
Abstract
Abstract: We obtain novel integral representations, expressed as contour integrals in the complex Fourier plane, for the solution of fully nonhomogeneous initial-boundary-value as well as interface problems for the Barenblatt–Zheltov–Kochina pseudo-parabolic equation of Sobolev–Galpern type formulated on the real line, half-line and finite interval. This fundamental partial differential equation (PDE) of mathematical physics emerges in a wide variety of natural phenomena and applied sciences including continuum mechanics, thermodynamics, chemical engineering, solid-state electronics, semi-conductor devices, battery research, and nanotechnology. A suitable implementation of a modern methodology, known as Unified Transform Method, is in force throughout this study, with particular challenges arising due to the higher-order mixed-derivative term of the PDE and the generality of the problems under consideration altogether. The boundary and interface conditions appear to be nonstandard but are naturally dictated by the structure of the PDE itself. Our explicit analytical formulae directly lend themselves to future explorations of the solutions’ qualitative properties such as asymptotic behavior, spatio-temporal dynamics, regularity and well-posedness. This work is expected to be of utility also in the investigation of nonlinear counterparts as well as towards the study of phase-transition phenomena and free-boundary problems, where the interface evolves dynamically according to energy balance laws.
Involved external institutions
National and Kapodistrian University of Athens
Greece (GR)
Ioffe Physical-Technical Institute / Физико-технический институт имени А. Ф. Иоффе РАН
Russian Federation (RU)
Hellenic Mediterranean University (HMU) / Τεχνολογικό Εκπαιδευτικό Ίδρυμα Κρήτης
Greece (GR)
Greece (GR)
Ioffe Physical-Technical Institute / Физико-технический институт имени А. Ф. Иоффе РАН
Russian Federation (RU)
Hellenic Mediterranean University (HMU) / Τεχνολογικό Εκπαιδευτικό Ίδρυμα Κρήτης
Greece (GR)
How to cite
APA:
Chatziafratis, A., Rukolaine, S.A., & Aifantis, E.C. (2026). Integral Representations for the Barenblatt–Sobolev–Galpern Pseudo-Parabolic Equation: Boundary-Value and Interface Problems on Unbounded and Finite Intervals. Russian Journal of Mathematical Physics, 33(3), 465-491. https://doi.org/10.1134/S1061920825601739
MLA:
Chatziafratis, A., S. A. Rukolaine, and E. C. Aifantis. "Integral Representations for the Barenblatt–Sobolev–Galpern Pseudo-Parabolic Equation: Boundary-Value and Interface Problems on Unbounded and Finite Intervals." Russian Journal of Mathematical Physics 33.3 (2026): 465-491.
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