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Ultraparabolic equations and unsteady heat transfer. (English) Zbl 1073.35139

Summary: The present paper is concerned with the boundary value problem for the equation \(\theta_t + \mathbf u\cdot \nabla\theta= \kappa \theta_{yy} + f\). Existence and uniqueness of the generalized solution are proved.

MSC:

35K70 Ultraparabolic equations, pseudoparabolic equations, etc.
35K20 Initial-boundary value problems for second-order parabolic equations
35D05 Existence of generalized solutions of PDE (MSC2000)
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