Bizhanova, Galina Irzhanovna Solutions in Hölder spaces of boundary-value problems for parabolic equations with nonconjugate initial and boundary data. (English. Russian original) Zbl 1282.35184 J. Math. Sci., New York 171, No. 1, 9-21 (2010); translation from Sovrem. Mat., Fundam. Napravl. 36, 12-23 (2010). Summary: The first and second one-dimensional boundary-value problems for parabolic equations are investigated in the case where the conjugation conditions for all required orders are not satisfied. The existence and uniqueness are proved. Estimates of solutions in classical and weighted Hölder spaces are obtained. We prove that the violation of conjugation for the given functions on the boundary of the domain at the initial-time moment causes the appearance of singular solutions. The order of singularity (as a power of \(t\)) is found for the singular solutions for \(t=0\). Cited in 4 Documents MSC: 35K20 Initial-boundary value problems for second-order parabolic equations 35B65 Smoothness and regularity of solutions to PDEs Keywords:one space dimension; singular solutions; order of singularity × Cite Format Result Cite Review PDF Full Text: DOI References: [1] M. Abramovitz and I. Stigan (Eds.), Handbook of Special Functions [in Russian], Nauka, Moscow (1979). [2] V. S. Belonosov, ”Estimates of the solutions of parabolic systems in Hölder weight classes and some of their applications,” Mat. Sb. (N.S.), 110 (152), No. 2, 163–188 (1979). · Zbl 0434.35056 [3] V. S. Belonosov and T. I. Zelenyak, Nonlocal Problems in the Theory of Quasilinear Parabolic Equations [in Russian], Novosibirsk. Gos. Univ., Novosibirsk (1975). · Zbl 0498.35045 [4] I. S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products, Elsevier–Academic Press, Amsterdam (2007). · Zbl 1208.65001 [5] O. A. Ladyženskaja, V. A. Solonnikov, and N.N. Ural’ceva, Linear and Quasilinear Equations of Parabolic Type, American Mathematical Society, Providence, R.I. (1967). [6] A. D. Polyanin, Handbook of Linear Equations of Mathematical Physics [in Russian], Fizmatlit, Moscow (2001). · Zbl 0989.35001 [7] V. A. Solonnikov, Bounds for the maximum modulus of derivatives for solutions of homogeneous parabolic initial-boundary problems, Preprint R-2-77, Leningrad. Otdel. Mat. Inst. Steklov. (1977). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.