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

Mesloub, Said; Lekrine, Nadia

Mat. Vesn. 53, No. 3-4, 79-89 (2001).

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.

Reviewer: Marko Nedeljkov (Novi Sad)

MSC:

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

Keywords:

singular boundary conditions; mixed problem for hyperbolic equation; strong solution; weighted \(L^2\) spaces