1. Solve the following first order partial differential equation with an initial condition. 1) , tuy...

 

  

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1. Solve the following first order partial differential equation with an initial condition. 1) ", tuy =ư, u(2,0) = a +2; u(x,0)=-4x + 1. 2) + uux = 0, 2. Let 2= B (0) be the upper half ball with center at the origin and radius 2. Let 22= B(0) be the upper half ball with center at the origin and radius 3 in R3. Find the harmonic function u(x) inside 2 satisfying the boundary condition: 3 √(x − 1)² + y(x + 1)² + (z − 1)² 1. Solve the following first order partial differential equation with an initial condition. 1) ", tuy =ư, u(2,0) = a +2; u(x,0)=-4x + 1. 2) + uux = 0, 2. Let 2= B (0) be the upper half ball with center at the origin and radius 2. Let 22= B(0) be the upper half ball with center at the origin and radius 3 in R3. Find the harmonic function u(x) inside 2 satisfying the boundary condition: 3 √(x − 1)² + y(x + 1)² + (z − 1)²

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