PDE:Laplace Transforms

solution $u_{t}=u_{{xx}}\,$

$u(x,0)=\partial (x)\,$ $-\infty <x<\infty \,$ $t>0\,$

LAPLACE TRANSFORM BOOKS

solution $u_{t}-u_{{xx}}=0\,$

$u(x,0^{+})=0\,$ $u(at,t)=g(t)\,$ $at\leq x<\infty \,$ $t>0\,$

solution $u_{t}=u_{{xx}}\,$

$u_{x}(0,t)=\alpha (t)\,$ $u(x,0)=0\,$ $x>0\,$ $t>0\,$

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