The analogy of the Saint-Venant's principle for the equation of the third order with multiple characteristics and their application (Q2742909)

Analogue of the Saint-Venant's principle for the third-order equation with multiple characteristics NEWLINE\[NEWLINE\frac\partial {\partial x}\Delta u+\sum_{i=1}^2\left(a_i(x,y,t) \frac{\partial^iu} {\partial x^i}+b_i(x,y,t) \frac{\partial^iu}{\partial y^i}\right)+ c(x,y,t)-u_t=0\tag{*}NEWLINE\]NEWLINE in the domain \(Q= \{(x,y)\mid x\in(0,\infty),y\in(0,l)\} \times(0,T)\) is considered. Boundary value conditions for (*) are taken in the form: \(u(x,y,0)=\varphi(x,y), u_{\mid x=0}=u_{x\mid x=0}= u_{\mid y=0}=u_{y\mid y=l}=0\). The uniqueness theorem in the domain \(Q\) among the functions growing in the infinity is proved.