On Nonlinear Heat-Conduction Equations with a Random Right Part

Cauchy problems for the nonlinear heat-conduction equations influenced by time noise in the form of stochastic integrals are investigated. It is shown that the solution of Cauchy problem for the stochastic nonlinear heat-conduction equation reduces to the solution of Cauchy problem for the nonlinear partial differential equation with random coefficients but without stochastic integrals. The work is based on the technique of symmetric integrals.