Anna Karczewska, Maciej Szczeciński
abstract:
In the paper, we consider a stochastic hybrid Korteweg-de Vries-Burgers type
equation with multiplicative noise in the form of cylindrical Wiener process. We
prove the existence of a martingale solution to the equation studied. The proof
of the existence of the solution is based on two approximations of the
considered problem and the compactness method. First, we introduce an auxiliary
problem corresponding to the equation studied. Then, we prove the existence of a
martingale solution to this problem. Finally, we show that the solution of the
auxiliary problem converges, in some sense, coincides to the solution of the
equation under consideration.
Mathematics Subject Classification: 93B05, 93C25, 45D05, 47H08, 47H10
Key words and phrases: KdV equation, Burgers equation, mild solution