Posted: Mon Dec 06, 2004 6:47 pm Post subject: A PDE proof

Consider the equation with third continuously differentiable, where is the flux.
Prove that if
for all and , then is a quadratic function of u.

Wilson

Frequent VisitorJoined: 20 Oct 2004Posts: 74

Posted: Thu Dec 16, 2004 11:09 am Post subject: Re: A PDE proof

If I regard u1 as a variable, then the equation in the given condition becomes an linear ODE in phi immediately. Then it can be solved to give a quadratic function of u. Is it correct?

Wilson

Frequent VisitorJoined: 20 Oct 2004Posts: 74

Posted: Sat Dec 18, 2004 7:47 am Post subject: Re: A PDE proof

Suppose and for all and ,
Taking , , and , we have

where is an arbitrary constant

Since , , and are independent of , therefore, is a quadratic function of .

Is it correct?

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