What values of the parameter $b$, $b>0$, does the problem $$u_{tt} = a^2u_{xx}$$$$u|_{t = 0}=0$$ $$u|_{t = bx}=0$$ have a zero solution in area: $x > 0, 0 < t < bx$.
I know for an equation: $$u_{tt}=u_{xx}+u_{yy}+f(t,x,y)$$ $$u|_{t=0} = u_1(x,y), u_t|_{t=0} = u_0(x,y)$$ solution has form:
$$u(t,x,y)= \frac{1} {2{\pi}} \int_{B_{t}(x,y)} \! \frac{u_1(\xi,\eta) d\xi d\eta} {\sqrt{t^2-(x-\xi)^2 - (y-\eta)^2}} + \frac{1} {2{\pi}} \frac{\partial}{\partial t} \int_{B_{t}(x,y)} \! \frac{u_0(\xi,η) d\xi d\eta} {\sqrt{t^2-(x-ξ)^2 - (y-\eta)^2}} + \frac{1} {2{\pi}}\int_0^t \int_{B_{t-\tau}(x,y)} \! \frac{f(\tau,\xi ,\eta) d\xi d\eta d\tau} {\sqrt{(t-\tau)^2-(x-\xi)^2 - (y-\eta)^2}}$$
This is a very difficult task for me and i do not know what to do next and how to solve this problem, please help me solve the problem, I have never solved such problems before.