On the shape of the solutions of second order parabolic partial differential equations (Q1122701)

The objective of this paper is to derive some properties of the solutions of an initial-boundary value problem for the following time-homogeneous equation in one spatial dimension: \(u_ t=(a\cdot u_ x)_ x+c\cdot u.\) A typical result under appropriate assumptions states that u(t,.) has at most finitely many zeros for every \(t>0\) (see Theorem 3.2). The proofs of the theorems essentially depend on the analyticity of the solutions with respect to the time variable.