Weak Solution of PDE

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Weak Solution of PDE
Generalized Derivatives
This definition is well posed in a sense, that if
function has a classical derivative then
Generalized derivative exist and almost every
where equal generalized equation ( Home Work,
prove this result)
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Sergey Lvovich Sobolev (1908-1989) ,
Soviet-Russian a founder of the approach
generalized derivatives and generalized solution
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Sobolev Space
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Generalized solution of the steady state
boundary problem second order PDE
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Implementation on FEMLAB a week formulation for
Elliptic PDE
Always be careful in choosing sign in weak
formulation check with respect to situation when
you have an analytical solution
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Generalized solution of the time dependent
Initial Boundary Problem (IBP) for second order
diffusive equation
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Implementation on FEMLAB a week formulation for
Parabolic PDE
Always be careful in choosing sign in weak
formulation check with respect to situation when
you have an analytical solution