Pde Definition and 743 Threads

regarding 1-d Head Equations on rods. I am aware of how to long a rod with length x=0 to x=L. and initial conditions of u(0,t)=0 degrees and u(L,t)=100 degrees. But how does the problem change if before t=0 the rod at x=0 was at 100 degrees and x=L was at 0 degrees. So at time=0 the rod was...

the physical meaning of the PDE?! Homework Statement http://agentsherrya.jeeran.com/qu.JPG Homework Equations How can I know the physical meaning of the following partial differential equation?!

Homework Statement Solve the equation u_{x}+2xy^{2}u_{y}=0 with u(x,0)=\phi(x) Homework Equations Implicit function theorem \frac{dy}{dx}=-\frac{\partial u/\partial x}{\partial u/\partial y}The Attempt at a Solution -\frac{u_x}{u_y}=\frac{dy}{dx}=2xy^2 Separating variables...

I want to know is it important to study D'Alembert solution? My main goal is to study Electromagnetics and wave equations, not the mechanical or heat equations. Seems like it is just one way of solving the PDE.

Finding basic solutions to a PDE?? So the problem is: x_o=0 \varphi'' + 4\varphi' + \lambda\varphi=0 which satisfies \varphi(0)=3 and \varphi'(0)=-1 I really don't even know where to start, I think its like an ODE right where we assume a solution, usually sin or an exponential and plug...

LaTex Code: \frac{\partial U}{\partial t} + ax\frac{\partial U}{\partial x} + b\frac{\partial^2 U}{\partial x^2} = 0 Can someone please tell me how to solve this PDE? Thanks, Geoff

What is the meaning of \;\;\frac{\partial u}{\partial t}(x,0) Is it equal to \;\;\frac{\partial u(x,t)}{\partial t}\;\;first\;then\;set\;t=0 or \;\;\;\frac{\partial u(x,0)}{\partial t}\;\; Which is setting t=0 in u(x,t) first then differentiate?

I don't have the answer of these question. Can someone take a look at a) and tell me am I correct? I don't even know how to solve b) [SIZE="6"]a)Homework Statement a) Show u(x,t)=F(x+ct) + G(x-ct) is solution of \frac{\partial^2 u}{\partial t^2}= c^2\frac{\partial^2 u}{\partial x^2}...

guys please help me, I'm trying to solve a simple moving PDE equation in matlab. The equation I'm trying to solve is dq(x,t)/dt=-c*dq(x,t)/dx with initial condition for example q(x,0)=exp(-(x-5)^2) c is a constant. What i want to do is to first discritize the initial condition with...

Hello friends please attached file to see my problem

Hallo, I must solve next set of PDE, which presents fluid flow. dP/dx=d/dx(mi*dv/dx)+d/dy(mi*dv/dy) dP/dy=d/dx(mi*du/dx)+d/dy(mi*du/dy) where mi=const with BC: v=v at x=0 u=u at y=0 Can you give me some hint? thanks j.

Homework Statement We are given f \epsilon C(T) [set of continuous and 2pi periodic functions] and PS(T) [set of piecewise smooth and 2pi periodic functions] SOlve the BVP ut(x,t) = uxx(x,t) ; (x,t) belongs to R x (0,inf) u(x,0) = f(x) ...

hey guys, i've reduced a more complex pde to the second-order linear equation u_t=u_xy, but now I'm a bit stuck! firstly, does anyone know if this equation has a proper name and thus been studied somewhere in the literature? secondly, any ideas on how to proceed with the general...

i have to solve this equation : du/dx * du/dy = x*y u(x,y) = x for y =0 with putting this equation in the form : F(x,y,u,du/dx,du/dy) = 0 . it can be solved. But mine book does not explain how to do this, there are no examples. Can someone help me ? or any links of examples on the...

Hi: I have the following PDE: ytzz=yzzzz+delta(t) With I.C.: t=0, y=0; and B.C.s: z=0, y=0,yzz=0; z=-x,y=0,yz=0 Can someone show me how to solve it? Kevin

Hi I have seen the expression for mass flow rate in one of the problems I am working on. I used to simply apply the expression for calculating the mass flow rate with respect to the position as (ρu + (∂u ∕∂x)dx) dy dz). ρ, u are density and velocity component respectively. I would like to...

Hey guys, I'm currently taking a Partial Differential Equations class, and for one assignment we have to come up with a model for a theoretical zombie outbreak. Well anyways, this is what I have gathered thus far: - I am defining my u(r,z,t) to be the population density of humans, where...

If z = f(x,y) and x = r \cos{v}, y = r\sin{v} the object is to show that d = \partial since it's easier to do on computer Show that: \frac{d^2 z}{dr^2} + \frac{1}{r} \frac{dz}{dr} + \frac{1}{r^2} \frac{d^2 z}{dv^2} = \frac{d^2 z}{dx^2} + \frac{d^2 z}{dy^2} It's from Adams calculus, will...

u_t=u_{xx}+2u_x 0<=x<=L, t>=0, u(x,0)=f(x), u_x(0,t)=u_x(L,t)=0 How to do this?

Hi I am having a lot of trouble trying to solve this equation. Any help is appreciated [SIZE="5"]x^2 \[partial]u/\[partial]x + 2 x \[partial]u/\[partial]t = g (t)

2Uxxy+3Uxyy-Uxy=0 where U=U(x,y) I made the substitution W=Uxy and then used a change of coordinates (n= 2x+3y, and r=3x-2y) which reduced the problem to solving Uxy=f(3x-2y)exp((2x+3y)/3) because W=f(r)exp(n/3). Now I have no idea where to go from there. Any help would be much appreciated...

uxx - x2 uyy = 0 (assume x>0) Is there any systematic method (e.g. change of variables) to solve this hyperbolic equation? dy/dx = [B + sqrt(B2 - AC)]/A => dy/dx = x => 2y -x2 = c dy/dx = [B - sqrt(B2 - AC)]/A => dy/dx = -x => 2y + x2 = k So the characteristic curves are 2y -x2 =...

Homework Statement x*u_{x} + y*u_{y}= 1 + y^2 u(x,1) = 1+ x; -infinity < x < +infinity Solve this parametrically and in terms of x and yHomework Equations We are supposed to solve this using the method of characteristics The Attempt at a Solution My problem is that solving the equation...

Homework Statement Use Fourier transforms to get solution in terms of f(t) adn g(t)Homework Equations d4u + K2*d2u =0 dx4 (space) dt2 u(0,t)=f(t) u'(0,t)=g(t) u''(L,t)=0 u'''(L,t)=0 The Attempt at a Solution I been working no it for hours the best I got is k4U...

Homework Statement Help, I don't know how to do the following question: Using Laplace to solve x' -y =1 2x' +x +y' = (t2-2t+1)e-(t-1) Homework Equations x(1)=0 y(3)=0 The Attempt at a Solution The problem I'm having is the initial conditions aren't at zero, and I'm not sure...

Hi all, I am Santosh, a grad student at FSU. I am trying to solve a system of 1-D pde's using finite difference scheme. Here's a brief description of my boundary conditions: Let my variables be S, T, V, & W, and k1, k2, k3, k4, k5, a, b, and c are constants. At x = 1,dA/dX = Ra, where...

I am confused by the following example about solving quasilinear first order PDEs. For the part I circled, the solution is just x^2 + y^2 = k where k is an arbitrary constant. To parametrize it in terms of t, can't we just put x = a cos(t), y = a sin(t) ? Here we only have one arbitrary...

Homework Statement Draw a picture to illustrate the two-dimensional drumhead in the x-y plane. Label the coordinates of the sides of the drumhead. Use this picture to illustrate the "modes" of vibration.Homework Equations \frac{\partial^{2}Z}{\partial x^{2}} + \frac{\partial^{2}Z}{\partial...

Homework Statement u_t = -{{u_{x}}_{x}} u(x,0) = e^{-x^2} Homework Equations The Attempt at a Solution The initial state is a bell curve centred at x=0. The second partial derivative of u at t=0 is {4x^2}{e^{-x^2}}, which is a Gaussian function, which means nothing to me other than its...

I have to solve: x(y^2 - z^2) \frac{\partial z}{\partial x} + y(z^2 - x^2) \frac{\partial z}{\partial y} + z(x^2 - y^2) So, I write out the characteristic system of ODEs: \frac{dx}{x(y^2 - z^2)} = \frac{dy}{y(z^2 - x^2)} = \frac{dz}{z(x^2 - y^2)}...

the question is , can a delta function /distribution \delta (x-a) solve a NOnlinear problem of the form F(y,y',y'',x) the question is that in many cases you can NOT multiply a distribution by itself so you could not deal with Nonlinear terms such as (y)^{3} or yy'

I've run across a PDE that (since I've failed to take a PDE class!) I'm finding some difficulty in solving. Does anyone have any suggestions? It's on a function R(r,t), with functions a(r,t) and b(r,t) and a constant k. If it's easier to solve with a and b not having t-dependence (just being...

Homework Statement Solve the problem. utt = uxx 0 < x < 1, t > 0 u(x,0) = x, ut(x,0) = x(1-x), u(0,t) = 0, u(1,t) = 1 Homework Equations The Attempt at a Solution Here is what I have so far but I'm not sure if I am on the right path or not. u(x,t) = X(x)T(t)...

Homework Statement Find the general solution to the PDE and solve the initial value problem: y2 (ux) + x2 (uy) = 2 y2, initial condition u(x, y) = -2y on y3 = x3 - 2 2. Homework Equations /concepts First order linear non-homogeneous PDEs The Attempt at a Solution I know that the...

Suppose we have a first order linear PDE of the form: a(x,y) ux + b(x,y) uy = 0 Then dy/dx = b(x,y) / a(x,y) [assumption: a(x,y) is not zero] The characteristic equation for the PDE is b(x,y) dx - a(x,y) dy=0 d[F(x,y)]=0 "F(x,y)=constant" are characteristic curves Therefore, the...

This is a question from a book in which I can't figure out, but it has no solutions at the back. Find the general solution to the PDE: xy ux + y2 (uy) - y u = y - x I've learned methods such as change of variables and characteristic curves, but I'm not sure how I can apply them in this...

Homework Statement Solve (Z+e^x)Z_x + (Z+e^y)Z_y = Z^2 - e^{x+y} Where Z = Z(x,y)Homework Equations Equations of the form PZ_x + QZ_y = R Where P = P(x,y,z) , Q=Q(x,y,z) , R=R(x,y,z) Are solved with the Lagrange method. It is possible to write this in the form: \frac{dx}{P} =...

I am new to non-linear PDEs. So I tried to solve it, but I stuck in the beginning. U^2_xU_t - 1 = 0 U(x, 0) = x

Homework Statement Quote: " PDE: ∂u/∂x + ∂u/∂y = 0 The general solution is u(x,y) = f(x-y) where f is an arbitrary function. Alternatively, we can also say that the general solution is u(x,y) = g(y-x) where g is an arbitrary function. The two answers are equivalent since u(x,y) = g(y-x) =...

[note: Ux=∂U/∂x, Uy=∂U/∂y] Example: Solve the partial differential equation 2Ux + 3Uy + U = 0 by using the change of variables V(x,y)=ln[U(x,y)] Solution: Vx = Ux/U Vy = Uy/U 2Ux + 3Uy + U = 0 Dividing both sides by U, we have 2Ux/U + 3Uy/U + 1 = 0 => 2Vx + 3Vy +1 = 0 => 2Vx + 3Vy...

Homework Statement Claim: The solution space of a linear homogeneous PDE Lu=0 (where L is a linear operator) forms a "vector space". Proof: Assume Lu=0 and Lv=0 (i.e. have two solutions) (i) By linearity, L(u+v)=Lu+Lv=0 (ii) By linearity, L(au)=a(Lu)=(a)(0)=0 => any linear...

Homework Statement I need to visualize the wave equation with the following initial conditions: u(x,0) = -4 + x 4<= x <= 5 6 - x 5 <= x <= 6 0 elsewhere du/dt(x,0) = 0 subject to the following boundary conditions: u|x=0 = 0 Homework Equations I'm not sure I understand the...

let be the PDE eigenvalue problem \partial_{t} f =Hf then if we define its Heat Kernel Z(u)= \sum_{n=0}^{\infty}e^{-uE_{n}} valid only for positive 'u' then my question is how could get an asymptotic expansion of the Heat Kernel as u approaches to 0 Z(u) \sim...

Homework Statement Derive the differential equation governing the longitudinal vibration of a thin cone which has uniform density p, show that it is 1/x/SUP] d/dx(x du/dx) = (1/c) d u/d[SUP]t Hint: The tensile force sigma = E du/dx where E is the Young's modulus (a constant), u is the...

Here is the problem: ∂v(s,n)/∂n + ∂u(s,n)/∂s + ∂ξ(s,n)/∂s + An dc(s)/ds = 0 (1) A1 ∂ξ(s,n)/∂n + ∂v(s,n)/∂s -c(s)+A2 v(s,n) + A3 c(s) = 0 (2) ∂u(s,n)/∂s + 2A2 u(s,n)=A2(ξ(s,n) + Anc(s)) -A1 ∂ξ(s,n)/∂s-A2nc(s) (3) Unknowns: u(s,n),v(s,n),ξ(s,n) Boundary conditions...

I have flipped through the first few pages of Evan's PDE book lately, and I am considering taking a graduate PDE course in the fall. However I don't really understand the purpose of PDE research. Not that I really understand the purpose of ODE research or even analysis research for that matter...

I am trying to decide between two different graduate math classes in the fall. These are the only classes that sound really interesting to me, as well as fitting in with the rest of my schedule. My other courses will consist of several physics type courses, notably, Jackson's electrodynamics...

I am trying to decide between two different graduate math classes in the fall. These are the only classes that sound really interesting to me, as well as fitting in with the rest of my schedule. My other courses will consist of several physics type courses, notably, Jackson's electrodynamics...

1. This problem concerns a nonhomogeneous second order linear ODE L[y] = g(t). Suppose that: y1(t) satisfies the ODE with the initial conditions y(0)=1, y'(0) = 0, y2(t) satisfies the ODE with the initial conditions y(0)=0, y'(0) = 1, and y3(t) satisfies the ODE with the initial conditions...

Hi. When solving a PDE by separation of variables, we obtain a collection of so-called normal modes. My book then tells me to make an "infinite linear combination" of these normal modes, and that this will be a solution to the PDE. But how do we know that this is in fact a solution? I have...