Geodesic
On Classical Solutions to Mixed Boundary Problems for One-dimensional Parabolic Equations of Second Order
Publications de l'Institut Mathématique, _N_S_67 (2000) no. 81, p. 53
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We prove the existence and uniqueness of classical solutions to mixed boundary problems for the equation $ \frac{\partial u}{\partial t}(x,t) - \frac{\partial^2u}{\partial x^2}(x,t) + q(x)u(x,t) = f(x,t) $ on a closed rectangle, with arbitrary self-adjoint boundary conditions. The initial function, the potential $q(x)$ and $f(x,t)$ belong to some subclasses of $W^{(k)}_p(\cdot)$ ($1
Classification : 35D15 
@article{PIM_2000_N_S_67_81_a5,
     author = {Neboj\v{s}a L. La\v{z}eti\'c},
     title = {On {Classical} {Solutions} to {Mixed} {Boundary} {Problems} for {One-dimensional} {Parabolic} {Equations} of {Second} {Order}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {53 },
     year = {2000},
     volume = {_N_S_67},
     number = {81},
     zbl = {0949.35063},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2000_N_S_67_81_a5/}
}
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Nebojša L. Lažetić. On Classical Solutions to Mixed Boundary Problems for One-dimensional Parabolic Equations of Second Order. Publications de l'Institut Mathématique, _N_S_67 (2000) no. 81, p. 53 . http://geodesic.mathdoc.fr/item/PIM_2000_N_S_67_81_a5/