How many boundary conditions does a pde need

But in comsol, I cannot just set one BC during setting the problem. This will cause a mathematical fallacy. And the result is also wrong. Your previous solution is to solve the ODE first, and set the BC at another end using the correct value. I think it is a kind of cheating, right? What is the physics behind your equation? Google a two point boundary value problem, and you'll see that there are no first order ODEs.

You are trying to do something unphysical. It is a simple quasi-1d compressible flow equation of motion with known pressure distribution and friction factor u: velocity of gas, unknown cf: 0.

But the comsol set it for me automatically. It seems that comsol cannot be used to solve IVP in 1d space. It is kind of obviously that since the equation already involves that derivative, we can not specify the same derivative in a different equation.

This can be used to eliminate f from the first of the equations, giving. The problem is that without additional conditions the arbitrariness in the solutions makes it almost useless if possible to write down the general solution. Nov 4 0 Rogers, Arkansas. Hi All, I've already asked this question in a different thread but that fetched only luke warm response.

Perhaps, my question was not very clear. I'm now starting this new thread after rephrasing my question so as to make my question clearer. How many boundary conditions are needed to solve a 2nd order PDE in x and y? For example, take the case of a 2D Laplace equation in x-y. It seems obvious that we need a total of 4 BC, 2 in x and 2 in y.

But, what is confusing to me is the relation between the number of BC and the shape of the domain on which the PDE is to solved? In fact, a large part of the solution process there will be in dealing with the solution to the BVP. Or maybe they will represent the location of ends of a vibrating string.

So, the boundary conditions there will really be conditions on the boundary of some process. We know how to solve the differential equation and we know how to find the constants by applying the conditions.

We mentioned above that some boundary value problems can have no solutions or infinite solutions we had better do a couple of examples of those as well here. This next set of examples will also show just how small of a change to the BVP it takes to move into these other possibilities.

This, however, is not possible and so in this case have no solution. So, with Examples 2 and 3 we can see that only a small change to the boundary conditions, in relation to each other and to Example 1, can completely change the nature of the solution. All three of these examples used the same differential equation and yet a different set of initial conditions yielded, no solutions, one solution, or infinitely many solutions.

Note that this kind of behavior is not always unpredictable however. Also, note that with each of these we could tweak the boundary conditions a little to get any of the possible solution behaviors to show up i. All of the examples worked to this point have been nonhomogeneous because at least one of the boundary conditions have been non-zero. The solution is then,. Because of this we usually call this solution the trivial solution.