PDE in ℝx(0,∞): Solving the Unknown

[Dubz]

The problem is a PDE
u_xx+u_yy= 0 in ℝx(0,∞)

what does this mean ℝx(0,∞) ?
Came across it in my math book, and I have not idea what to google to find this.

 

[fresh_42]

The problem is a PDE
u_xx+u_yy= 0 in ℝx(0,∞)

what does this mean ℝx(0,∞) ?
Came across it in my math book, and I have not idea what to google to find this.

It probably means the set $\{(x,y) \in \mathbb{R}^2\,\vert \,y>0\} = \mathbb{R} \times \mathbb{R}_+\,.$

 

[protonsarecool]

To answer your google question, it is called the Cartesian product. As fresh said, it is just the set of ordered tuples.