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On a nonlocal singular mixed evolution problem. (English) Zbl 1093.35517

The authors deal with a singular mixed problem for the equation \(u_{t_1t_2}-\frac1x(xu_x)_x=F(x,t_1,t_2)\), \(t_1\in(0,T_1)\), \(t_2\in(0,T_2)\), \(x\in(0,a)\), \(T_1,T_2,a<\infty\). After giving the definition of a strong solution, they prove the existence and uniqueness of such a solution. Weighted \(L^2\) spaces and a priori estimates are used in proving these assertions.

MSC:

35L20 Initial-boundary value problems for second-order hyperbolic equations
35B45 A priori estimates in context of PDEs
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