Pde Definition and 743 Threads

Hi, I'm really interesting of PDE, but I don't really know what I have to learn before start with PDE. I have learn multivariable calculus and ODE, but are there something need to learn before PDE? Thanks in advance.

Hi, Say I have this pde: u_t=\alpha u_{xx} u(0,t)=\sin{x}+\sin{2x} u(L,t)=0 I know the solution for the pde below is v(x,t): v_t=\alpha v_{xx} v(0,t)=\sin{x} v(L,t)=0 And I know the solution for the pde below is w(x,t) w_t=\alpha w_{xx} w(0,t)=\sin{2x} w(L,t)=0 Would...

Hi Everyone, I was reading a paper and I found it hard to comprehend how some of the equations were arrived at, probably because my math rottenness. Anyway I need your help on understanding how these equations were arrived at. The problem goes like this: We have this PDE in cylindrical...

Homework Statement Solve u_t -k u_xx +V u_x=0 With the initial condition, u(x,0)=f(x) Use the transformation y=x-Vt Homework Equations The solution to the equation u_t - k u_xx=0 with the initial condition is u(x,t)=1/Sqrt[4\pi kt] \int e^(-(x-y)^2 /4kt)f(y) dy The Attempt at a...

In my research work, I recently have come across a system of three linear first order pde's whose characteristic polynomial has one real and two complex conjugate zeros. I have searched the available resources and could nowhere find out which category (elliptic/hyperbolic/parabolic) it falls...

I was looking through a calculus book doing some of the practice problems where I was asked to calculate the curl of a few functions. One of them got me thinking, is there a function whose curl is itself? Much like how e^{x} is it's own derivative, is there a vector field that is it's own curl...

anyone have any ideas on a technique to tackle this PDE: u_{tt} = u_{xx} + u_{xxxx} its like a 4th order wave equation any help or references would be appreciated

Homework Statement Consider the PDE which has the solution The Attempt at a Solution So what I am having trouble is solving it using this method. I am going to say that my $$u(x,t) = \sum_{n=1}^{\infty} u_n(t) \sin(nx)$$ and $$x \sin(t) =...

Hi!This is a quite sophisticated problem, but it’s interesting and challenging! Consider the following case: Let’s say we have a 3-dimensional disk with a radius r_{2} and a thickness d (so it actually is a cylinder with a quite short height compared to radius). We’re interested in solving...

I just graduated with a B.S. Math and Physics Minor. I took Probability but not Statistics. I also didn't get a chance to take PDE. I'm looking for some good textbooks on the subjects.

Hi all! I'm stuck with a system of PDE. I'm not sure I want to write it here in full, so l'll write just one of them. I've found a solution to this equation but I'm not sure it's the most general one since when I plug this solution into the other eqs, I get a trivility condition for the...

Hi all, I have a system of 3 coupled linear PDEs which can be expressed in matrix form as: \left( \begin{array}{ccc} \alpha_1 \partial_{\theta} & \alpha_2 & \alpha_3 \\ \beta_1 \partial_r & \beta_2 & \beta_3 \\ 0 & \gamma_2 \partial_{\theta} & 1 + \gamma_3 \partial_r \\ \end{array}...

Homework Statement solve x2ux + y2uy = 0 for u(2,y) = y Homework Equations The Attempt at a Solution with a = x2 and b = y2 y' = b/a = (y/x)2 this can be solved for y by separation of variables: y = \frac{x}{1-xC} and C = \frac{y-x}{xy} now u(x,y) = f(C) = f(\frac{y-x}{xy}) applying...

Hi, my equation is; \frac{\partial}{\partial t}U(x,y,t) = 2g \left( x \frac{\partial}{\partial y} - y \frac{\partial}{\partial x} \right) U(x,y,t) I want to find the general solution to this but I don't know how to find it? Any help would be great...thanks :D

I am taking it in a few weeks, could someone tell me which topic are generally more challenging? PDE is Partial Differential Equations. Thank you

I'll be taking PDE this coming Fall semester, and I want to have a head start by doing some self studying this summer. What's a good textbook you would recommend for PDE? (the official textbook in my university is "Beginning Partial Differential Equations" by Peter O'Neil but I've heard...

Hi, I have a test tomorrow and I'd like you to guys help me please. Solve the following: $\begin{align*} & {{u}_{tt}}={{u}_{xx}}+1+x,\text{ }0<x<1,\text{ }t>0. \\ & u(x,0)=\frac{1}{6}{{x}^{3}}-\frac{1}{2}{{x}^{2}}+\frac{1}{3},\text{ }{{u}_{t}}(x,0)=0,\text{ }0<x<1. \\ &...

I haven't worked with partial derivatives since high school 25 years ago so I'm quite a bit rusty and need a little guidance. I'm reading through a paper and would like to write a program to simulate it. The equations are: Eq 1. Eq 13. M=f*Po+f*(Pb-Po)*(1-ln(e)^(-0.693*time/Halftime) Eq 10...

Ok I have read/browse 3 books so far about PDEs. They separate variables. Then they suddenly go. solution is X= some thing sin some thing cos Y= some thing -ek some thing ek Where do sine and cos comes from ? How do they know?? where is it explained?

Hi, Can somebody help me solve the following PDE? ∂p(x,t)/∂t = -p(x,t) + ∫λ(x-x')p(x',t)dx' with p(x,0)=δ(x) Thanks a lot

Hi, I am a master student comes from USM in Malaysia. I don't know my problem should placed on differential forum or high energy physics forum. Anywhere, My current study is high energy physics subject and my main study is focus on monopole instanton solution in static form which did not...

Hello! I would like to find some functions F(x,y) which satisfy the following equation \frac{F(x,y)}{\partial x}=\frac{F(y,x)}{\partial y} For example this is obviously satisfied for the function F= exp(x+y) I would like however to find the most general closed form solution...

Hi, I'm currently working on a thesis in Economics. I have stumbled upon a system of differential equations that needs to be solved. I am stuck, and have trouble getting the right help from my advisor who is also not very acquainted with numerical methods. For the past couple of days I have...

pure and mixed, what do they tell you about a function?

Hi, I have the following PDE-S\frac{\partial\vartheta}{\partial\tau}+\frac{1}{2}\sigma^2\frac{X^2}{S}\frac{\partial^2\vartheta}{\partial\xi^{2}} + [\frac{S}{T} + (r-D)X]\frac{\partial\vartheta}{\partial\xi}I am asked to seek a solution of the form \vartheta=\alpha_1(\tau)\xi + \alpha_0(\tau)...

Hi everyone, I am doing a sheet on Asian Options and The Black Scholes equation. I have the PDE, \frac{∂v}{∂τ}=\frac{1}{2}σ^{2}\frac{X^{2}}{S^{2}}\frac{∂^{2}v}{∂ε^{2}} + (\frac{1}{T} + (r-D)X)\frac{∂v}{∂ε} I have to seek a solultion of the form v=α_{1}(τ)ε + α_{0}(τ) and determine...

Hi group, In order to understand the methods of characteristics, I've been reading its wiki entry plus other sources. However, one of the first step of finding the normal surface vector given the PDE remains baffling to me in terms of how it's derived. In short, when provided with a(x...

Hello, I have the PDE \frac{-∂v}{∂τ}+\frac{1}{2}σ^{2}ε^{2}\frac{∂^{2}v}{∂ε^{2}}+(\frac{1}{T}+(r-D)ε)\frac{∂v}{∂ε}=0 and firstly I need to seek a solution of the form v=α_{1}(τ)ε + α_{0}(τ) and then determine the general solution for α_{1}(τ) and α_{0}(τ). I am given that ε=\frac{I}{TS}...

I have a PDE in two variables, u and v, which takes the form \frac{\partial\psi}{\partial u\hspace{1pt}\partial v} + \frac{1}{r}\left(\frac{\partial r}{\partial u} \frac{\partial \psi}{\partial v} + \frac{\partial r}{\partial v}\frac{\partial\psi}{\partial u}\right) for an auxiliary...

Hi, I'm an undergrad in EE who wants to learn the basics of solving PDEs (and Fourier series/transforms), but who has some learning disabilities (developmental, most notably). Before I get criticism for what I'm about to say (which will be asking for an alternative to the obligatory "read...

Hi, I know from basic math courses that inverse trig functions are multi valued (e.g. arctan(c)=θ+n*2∏). Now, if I solve a partial differential equation and I get an inverse trig function as part of my solution, does that mean solutions to the pde are non-unique? For example, if...

Solve $u_x+2u_y+2u=0,$ $x,y\in\mathbb R$ where $u(x,y)=F(x,y)$ in the curve $y=x.$ I don't know what does mean with the $y=x.$ Well I set up the following $\dfrac{dx}{1}=\dfrac{dy}{2}=\dfrac{du}{-2} ,$ is that correct? but I don't know what's next. Thanks for the help!

Hi, need some help here so thanks to any replies. PDE: $$yu_x+2xyu_y=y^2$$ edit: Forgot to mention the condition $$u(0,y)=y^2$$ a) characteristic equations: $$dx/ds=y$$ $$dy/ds=2xy$$ $$du/ds=y^2$$ b) find dy/dx and solve $$dy/dx=dy/ds * ds/dx = x/y$$ $$ydy=xdx$$ $$y^2/2=x^2/2 +c$$ $$y=\pm...

Given $\begin{aligned} & {{u}_{t}}={{u}_{xx}},\text{ }x>0,\text{ }t>0 \\ & u(x,0)={{u}_{0}}, \\ & {{u}_{x}}(0,t)=u(0,t). \end{aligned} $ I need to apply the Laplace transform to solve it. I'll denote $u(x,s)=\mathcal L(u(x,\cdot))(s),$ so for the first line I have $s\cdot...

Dear MHB members, I have the following equation $xy(z_{xx}-z_{yy})+(x^{2}-y^{2})z_{xy}=yz_{x}-xz_{y}-2(x^{2}-y^{2})$. When I transform this into the canonical form via $\xi=2xy$ and $\eta=x^{2}-y^{2}$, I obtain...

Hi everyone! I want to design a robust controller for a system which is driven by a PDE. I need to acquire its transfer function in 's' parameter which means it should be transferred by Laplace transformation. I know that the result transfer function will be an infinite series of transfer...

Homework Statement I'm just trying to get an understanding of answering PDEs, so wanted to ask what you thought of my answer to this question. The one-dimensional wave equation is given by the first equation shown in this link; http://mathworld.wolfram.com/WaveEquation1-Dimensional.html...

Homework Statement The one-dimensional heat diffusion equation is given by : ∂t(x,t)/∂t = α[∂^2T(x,t) / ∂x^2] where α is positive. Is the following a possible solution? Assume that the constants a and b can take any positive value. T(x,t) = exp(at)cos(bx) Homework Equations...

Let $u\in\mathcal C^1(\overline R)\cap \mathcal C^2(R)$ where $R=(0,1)\times(0,\infty).$ Suppose that $u(x,t)$ verifies the following wave equation $u_{tt}=K^2 u_{xx}+h(x,t,u)$ where $K>0$ and $h$ is a constant function. a) Determine the total energy of the string. (Well I don't know what does...

Solve $\begin{aligned} & {{u}_{tt}}={{u}_{xx}}+1+x,\text{ }0<x<1,\text{ }t>0 \\ & u(x,0)=\frac{1}{6}{{x}^{3}}-\frac{1}{2}{{x}^{2}}+\frac{1}{3},\text{ }{{u}_{t}}(x,0)=0,\text{ }0<x<1, \\ & {{u}_{x}}(0,t)=0=u(1,t),\text{ }t>0. \end{aligned} $ Here's something new for me, the boundary...

Solve $\begin{aligned} & {{u}_{tt}}={{c}^{2}}{{u}_{xx}}+A{{e}^{-x}},\text{ }0<x<L,\text{ }t>0, \\ & u(0,t)=B,\text{ }u(L,t)=M,\text{ }t>0, \\ & u(x,0)=0={{u}_{t}}(x,0),\text{ 0}<x<L. \end{aligned} $ What do I need to do first? Homogenize the first boundary conditions? Or first making the...

Consider the equation $\begin{aligned} & {{u}_{t}}=K{{u}_{xx}}+g(t),\text{ }0<x<L,\text{ }t>0, \\ & {{u}_{x}}(0,t)={{u}_{x}}(L,t)=0,\text{ }t>0 \\ & u(x,0)=f(x), \\ \end{aligned} $ a) Show that $v=u-G(t)$ satisfies the initial value boundary problem where $G(t)$ is the primitive of...

I'm confused on what classes to take next semester. I've talked to my adviser but they're kinda useless as they don't want me to take upper level courses (past calc 3 and ODE). However, I want a dual math and physics degree which would be helpful in gradschool. Right now I have the following...

Nowadays people usually consider PDEs in weak formulations only, so I have a hard time finding statements about the existence of classical solutions of the Poisson equation with mixed Dirichlet-Neumann boundary conditions. Maybe someone here can help me and point to a book or article where I...

Homework Statement Find the Riemann function for uxy + xyux = 0, in x + y > 0 u = x, uy = 0, on x+y = 0 Homework Equations The Attempt at a Solution I think the Riemann function, R(x,y;s,n), must satisfy: 0 = Rxy - (xyR)x Rx = 0 on y =n Ry = xyR on x = s R = 1 at (x,y) = (s,n) But I...

I have a battle with the following direct partial integration and separation of variables toffee: I have to solve, u(x,y)=\sum_{n=1}^{∞}A_n sin\lambda x sinh \lambda (b-y) If there were no boundary or initial conditions given, do I assume that λ is \frac{n\pi}{L} and do I then solve A_n...

Homework Statement Classify the equation and use the change of variables to change the equation to the form with no mixed second order derivative. u_{xx}+6u_{xy}+5u{yy}-4u{x}+2u=0 Homework Equations I know that it's of the hyperbollic form by equation a_{12}^2 - a_{11}*a_{22}, which...

Hello everyone, I am trying to model the process of laser ablation on a material using MATLAB. The governing equation is of the form: ∂T(x,t)/∂t = ∂/∂x(A*∂T/∂x) + B*exp(-C*t2)*exp(-D*x) with one Initial condition and two boundary conditions. Using the built-in 'pdepe' function in Matlab...

Homework Statement A square rectangular pipe (sides of length a) runs parallel to the z-axis (from -\infty\rightarrow\infty). The 4 sides are maintained with boundary conditions (i) V=0 at y=0 (bottom) (ii) V=0 at y=a (top) (iii) V=constant at x=a (right side) (iv) \frac{\partial...

Homework Statement Mathews and Walker problem 8-2 (page 253): Assume that the neutron density n inside U_{235} obeys the differential equation \nabla ^2 n+\lambda n =\frac{1}{\kappa } \frac{\partial n }{\partial t} (n=0 on surface). a)Find the critical radius R_0 such that the neutron density...