Substantiation of the perturbation method for a quasilinear heat-conduction problem (Q1571174)

The authors rigorously substantiate a regular perturbation algorithm as applied to a quasilinear time-dependent heat-conduction problem. It is formulated a perturbed problem containing a small parameter \(\varepsilon\) and proved the existence and uniqueness of the solution to the perturbed problem in a certain class of functional spaces. The authors obtain sufficient conditions for the initial data, under which the solution to the problem can be represented as a convergent series in powers of \(\varepsilon\), including \(\varepsilon=1\). The results of numerical experiments are presented.