On a Fourth Order Parabolic Equation with Mixed Type Boundary Conditions in a Nonrectangular Domain

• Published in: Moroccan journal of pure and applied analysis Vol. 1; no. 2; pp. 76 - 90
• Main Author: Kheloufi, Arezki
• Format: Journal Article
• Language: English
• Published: Fez,Morocco University Sidi Mohamed Ben Abdallah 01.12.2015; De Gruyter Open; De Gruyter Poland; Sciendo
• Subjects: Analysis; Anisotropic weighted Sobolev spaces; Higher-order parabolic equations; Mathematics; Mathematics and Statistics; Mixed type conditions; Nonregular domains; Research Article; Anisotropic weighted Sobolev spaces; Mixed type conditions; Higher-order parabolic equations; Nonregular domains
• ISSN: 2351-8227; 2605-6364; 2351-8227
• DOI: 10.7603/s40956-015-0006-5

This paper is devoted to the study of the following fourth order parabolic equation in the non-necessarily rectangular domain The equation is subject to mixed type conditions , on the lateral boundary of Q . The right-hand side term f of the equation lies in the space of square-integrable functions on Q with the measure ωdtdx . Our aim is to find sufficient conditions on the coefficient β and on the functions φ i ; i = 1; 2 and on the weight ω such that the solution of this equation belongs to the anisotropic Sobolev space The analysis is performed by using the domain decomposition method.