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What is Linear Homogeneity in Quxt Equation about?

The document considers the partial differential equation ∂u/∂t = k^2 + ∂^2u/∂x^2 + α(x,t)u + β(x,t). It aims to show that this equation is linear and homogeneous when β(x,t)=0. It first writes the equation in operator form L(u)=∂u/∂t - k^2 - ∂^2u/∂x^2 - α(x,t)u. It then shows that L(c1u1 + c2u2)=c1L(u1)+c2L(u2), proving the operator L is linear.

Author

neeti

Language

EN