Sinsoysal B.Rasulov M.2024-03-132024-03-1320202666-8181https://doi.org/10.1016/j.padiff.2020.100002https://hdl.handle.net/20.500.12662/3020In this study using the residue method the solution of the first type mixed problem for 2D linear parabolic equation in the bounded cylinder of the Euclidean space R3(x,y,t) is obtained in explicit form. When the smoothness of initial data does not permit to construct of the classical solution then it is necessary to extend the concept of classical solution. Based on the examined problem is proved that the obtained solution is a weak solution too. The use of this proof method to prove the existence of a weak solution can be applied to prove the existence of weak solutions for the more general problem with non-self-adjoint and even that contains higher-order derivative with respect to t in the boundary condition. © 2020 The Author(s)eninfo:eu-repo/semantics/openAccessExpansion formulaResidue methodWeak solutionArticle10.1016/j.padiff.2020.1000022-s2.0-85125854599Q21