The explosion of the solutions of stocastic heat equations

In this thesis, nonlinear stochastic wave and heat equation are studied. For this purpose, stochastic wave and heat equation and history are given in the first chapter. In the second chapter, we present the literature about the stochastic wave and heat equation. In the third chapter, we give information about the basic mathematical description, theorems and lemma. In the fourth chapter, general information about blow-up of stochastic wave and heat equations is given. In the fifth chapter, the previously studied parabolic type nonlinear stochastic heat equation is shown to be the blow-up of the solution by using appropriate energy inequalities. The sixth chapter is the original part of this thesis. The solution of the nonlinear stochastic wave equation exploded. In our study, appropriate energy inequalities are used to determine whether the solution exists in finite and infinite time. The results obtained in the seventh chapter are summarized and some recommendations are made.