Construction of the fundamental solution of disturbed parabolic equation
In the present work the problem of construction of a fundamental solution \(e^{t(L+L_1)}\) of the equation \(u_t=(L+L_1)u\) is considered. The operators \(L\) and \(L_1\) are elliptic ones and the properties of the evolution operator \(e^{tL}\) of a non-disturbed equation \(u_t=L u\) are assumed to be known. The construction is reduced to an iterative procedure the convergence of which is proved. Two examples of perturbed parabolic equations are considered.
scientific article; zbMATH DE number 1981553
scientific article