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

[1] Amster P., Jüngel A., Matthes D.B.-K. Non-homogeneous boundary conditions for a fourth-order diffusion equation. C. R. Acad. Sci. Paris, Ser. 2008, (I) (346): 143-14810.1016/j.crma.2007.12.001Search in Google Scholar

[2] Baderko E. A. On the solution of the boundary value problems for parabolic equations of high order in domains with curvilinear lateral boundaries. Diff, Urav., 1976, 12(2):1781-1792Search in Google Scholar

[3] Baderko, E. A. On the solution of boundary value problems for linear parabolic equations of arbitrary order in noncylindrical domains by the method of boundary integral equations [Ph D Thesis]. Moscow, 1992Search in Google Scholar

[4] Besov V. The Continuation of Function in L1 p and W1 p . Proc. Steklov Inst. Math., 1967, (89):5-17Search in Google Scholar

[5] Cherepova M. F. On the solvability of boundary value problems for a higher order parabolic equation with growing coefficients. Doklady Mathematics, 2006, 74(3):819-82010.1134/S1064562406060093Search in Google Scholar

[6] Cherepova M. F. Regularity of solutions of boundary value problems for a second-order parabolic equation in weighted H¨older spaces. Differential Equations, 2013, 1 (49):79-8710.1134/S0012266113010084Search in Google Scholar

[7] Galaktionov V. A. On regularity of boundary point for higer-order parabolic equations: towards Petrovskii-type criterion by blow-up approach, Nonlinear Differential Equations and Applications, 2009, (16):597-65510.1007/s00030-009-0025-xSearch in Google Scholar

[8] P. Grisvard, Singularities in Boundary Values Problems, Masson, Paris, 1992Search in Google Scholar

[9] Kheloufi, A. Study of the first boundary value problem for a fourth order parabolic equation in a nonregular domain of RN+1, TWMS J. App. Eng. Math., 2015, 1(5): 145-157Search in Google Scholar

[10] Kheloufi, A. On a fourth order parabolic equation in a nonregular domain of R3. Mediterr. J. Math. 2015, (12): 803-82010.1007/s00009-014-0429-7Search in Google Scholar

[11] Kondratiev, V.A. Boundary value problems for parabolic equations in closed regions. Trans. Moscow Math. Soc., vol. 15, Am. Math. Soc., Providence, RI, 1966, pp. 450-504Search in Google Scholar

[12] Kondratiev, V.A.: Boundary value problems for elliptic equations in domains with conical or angular points. Trans. Moscow Math. Soc., vol. 16,Am.Math.Soc., Providence, RI, 1967, pp. 227-313 Search in Google Scholar

[13] Labbas, R., Sadallah, B.-K.: Smoothness of the solution of a fourth order parabolic equation in a polygonal domain. Int. J. Appl. Math. 1999, (1):75-90Search in Google Scholar

[14] Ladyzhenskaya O. A., Solonnikov V. A., Ural’tseva N. N. Linear and Quasi-Linear Equations of Parabolic Type. A.M.S., providence, Rhode Island, 196810.1090/mmono/023Search in Google Scholar

[15] Lions J. L., Magenes E. Problèmes aux Limites Non Homogènes et Applications, 1, 2. Dunod, Paris, 1968Search in Google Scholar

[16] Mikhailov, V.P. The Dirichlet problem for a parabolic equation, I. Mat. Sb. (N.S.) 61(103), 40-64 (1963)Search in Google Scholar

[17] Mikhailov, V.P. The Dirichlet problem for a parabolic equation, II. Mat. Sb. (N.S.), 1963, 62(104): 140-159Search in Google Scholar

[18] Sadallah B.-K. Etude d’un problème 2m-parabolique dans des domaines plan non rectangulaires. Boll. Un. Mat. Ital., 1983, 2-B(5):51-112Search in Google Scholar

[19] Sadallah B.-K. High order regularity of the singularities of the solution of a parabolic equation in a singular domain, Kuwait Journal of Sciences and Engineering, 1997, (24): 185-198Search in Google Scholar

[20] Sadallah B.-K. Singularities of the solution of a 2m-parabolic problem in a polygonal domain, Arab Journal of Mathematical Sciences, 1998, 2(4):31-41 Search in Google Scholar