Geodesic
Solutions in Hölder spaces of boundary-value problems for parabolic equations with nonconjugate initial and boundary data
Contemporary Mathematics. Fundamental Directions, Proceedings of the Fifth International Conference on Differential and Functional-Differential Equations (Moscow, August 17–24, 2008). Part 2, Tome 36 (2010), pp. 12-23 
G. I. Bizhanova. Solutions in Hölder spaces of boundary-value problems for parabolic equations with nonconjugate initial and boundary data. Contemporary Mathematics. Fundamental Directions, Proceedings of the Fifth International Conference on Differential and Functional-Differential Equations (Moscow, August 17–24, 2008). Part 2, Tome 36 (2010), pp. 12-23. http://geodesic.mathdoc.fr/item/CMFD_2010_36_a1/
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     author = {G. I. Bizhanova},
     title = {Solutions in {H\"older} spaces of boundary-value problems for parabolic equations with nonconjugate initial and boundary data},
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     pages = {12--23},
     year = {2010},
     volume = {36},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2010_36_a1/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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 $t=0$.

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