Pde Definition and 743 Threads

[b]1. A function "v" where v(x,y,z)≠0 is called an eigenfunction of the Laplacian Δ (on some region Ω - with specified homogenous BC) if v satisifies the BC ad also Δv=-λv on Ω for some number λ. Part A: Give an example of an eigenfunction of Δ when Ω is the cube [0,∏]3 with Dirichlet BCs...

I'm a rising math major with a developing interest in General Relativity. I think the idea of studying Relativity from a mathematicians perspective sounds very appealing for graduate work. Besides differential geometry and partial differential equations, what are the most relevant pure math...

Homework Statement Solve \frac{\partial \phi}{\partial t} + \phi \frac{\partial \phi}{\partial x} - \infty < x < \infty , t > 0 subject to the following initial condition \phi (x,0) = \left\{ \begin{array}{c} 1,\; x<0\\ 1-x,\;0\leq x<1\\ 0,\; x\geq1\end{array}\right. Homework...

Hello, I derived a model in the form \begin{array}{rcl}\frac{\partial U(\vec{x},t)}{\partial t}&=&\gamma^2\Vert\nabla U(\vec{x},t)\Vert,\\\int_{\Omega}U(\vec{x},t)\, d \Omega&=&U_0,\quad\forall t\\U(\vec{x},0)&=&f(\vec{x}).\end{array} I don't know to solve that. THanks for help.

I just had a 'quiz' in my PDE class today and there was a problem my friends and I are convinced has no explicit solution. I want to know if maybe we are doing something wrong? Homework Statement (x+y)u_{x} + yu_{y} = 0 [/itex] u(1,y) = \frac{1}{y} + ln(y) [/itex]Homework Equations ...The...

I have the PDE: (v_r)^2+(v_z)^2=p^2 where v=v(r,z), p=p(r,z). I have some boundary conditions, of sorts: p=c*r*exp(r/a)exp(z/b) for some constants a,b,c, at r=infinity and z=infinity p=0 at f=r, where (f_r)^2=p*r/v-v*v_r (f_z)^2=p*r/v+v*v_r Is it possible that one could obtain an...

Here's my question: as soon as I learned Quantum Mechanics and Schrodinger equation, I saw a "similarity" with the equation one gets in classical mechanics for the evolution of a function in phase space. In QM one has: i\hbar\frac{d}{dt}\psi = \hat{H}\psi and this is a evolution...

Okay, kind of a silly question...but what do all of these stand for? ODE=Ordinary Differential Equations ( ;O I hope this is right, I took a course on this stuff) PDE=Partial Differential Equations ( Hope this is right too, taking this next semster) DDE=...? SDE=...? DAE=...

The problem: Solve for u(x,y,z) such that xu_x+2yu_y+u_z=3u\; \;\;\;\;u(x,y,0)=g(x,y) So I write \frac{du}{ds}=3u \implies \frac{dx}{ds}=x,\; \frac{dy}{ds}=2y\;\frac{dz}{ds}=1 . Thus u=u_0e^{3s},\;\;x=x_0e^{s}\;\;y=y_0e^{2s}\;\;z=s+z_0 but from here I can't figure out what to do, there...

Homework Statement u_{t}=3u_{xx} x=[0,pi] u(0,t)=u(pi,t)=0 u(x,0)=sinx*cos4x Homework Equations The Attempt at a Solution with separation of variables and boundry conditions I get: u(x,t)= \sumB_{n}e^-3n^{2)}}*sinnx u(x,0)=sinx*cos4x f(x)=sinx*cos4x=\sumB_{n}*sinnx...

Homework Statement Suppose that u(x,y) is a solution of Laplace's equation. If \theta is a fixed real number, define the function v(x,y) = u(xcos\theta - ysin\theta, xsin\theta + ycos\theta). Show that v(x,y) is a solution of Laplace's equation. Homework Equations Laplace's equation...

I was given the equation dp/ds = 4 + 1/e*d/de(e*dp/de) The derivatives in the equation are partial derivatives the values of p,s,e are dimensionless numbers. I am to assume that the solution is separable and then use finite difference method to solve for p, the finite difference method...

unknown in PDE! Hi, I'm solving a problem which determines the flow between a porous material and an impermeable material, using the slip-flow boundary conditions as proposed by Beavers and Joseph in '67. I can solve the whole problem as stated below, which gives the velocity u of the fluid...

I believe that this is similar to the proof of schrodinger equation to obtain quantum numbers, however i cannot seem to understand the relationship between n, l and m: I have attached a pdf file on partial differential equations and on page 5, i cannot seem to understand why it is +n^2 and...

Homework Statement sin(y)\frac{ \partial u}{ \partial x} + \frac{ \partial u}{ \partial y} = (xcos(y)-sin^2(y))u where ln(u(x,\frac{\pi}{2})) = x^2 + x - \frac{\pi}{2} for -1 \leq x \leq 3 determine the characteristic curves in the xy plane and draw 3 of them determine the general...

Homework Statement Solve the initial boundary value problem: u_t + cu_x = -ku u is a function of x,t u(x,0) = 0, x > 0 u(0,t) = g(t), t > 0 treat the domains x > ct and x < ct differently in this problem. the boundary condition affects the solution in the region x < ct, while...

Hi guys tryin to study for a pde exam and cannot solve this question Find a general solution of the equation exp(-x)dz/dx+{/y(squared)}dz/dy=exp(x)yz (ii) Solve the Cauchy problem, i.e. find the integral surface of this equation passing through the curve . y = ex/3 , z = e ...

1. Integrate (by calculus): u''(x) = -4u(x), 0 < x < pi 2. The attempt at a solution I'm not really sure where to start on this one is my problem. I can see that it won't be a e^2x problem because of the negative, which leads me to believe that it will deal with the positive/negative...

Hi I have a set of two linearized integro-partial-differential equations with derivatives of first order (also inside the integrals). How many boundary (initial) conditions should I give for such problem for the solution to be unique? is the 'initial condition that intersect once with the...

Homework Statement Consider the PDE ut + 6u3ux + uxxx = 0 which may be thought of as a higher-order variant of the KdV. a) Assume a traveling wave u = f(x-ct) and derive the 3rd-order ODE for that solution. b) Reduce the order of this ODE and obtain the expression for the polynomial g(f)...

Suppose I have the PDE: \frac{\partial^{2}u}{\partial x^{2}}+\frac{\partial^{2}u}{\partial y^{2}}=\frac{1}{c^{2}} \frac{\partial^{2}u}{\partial t^{2}} with u(0,x,y)=\partial_{t}u(0,x,y)=0 along with u(t,0,y)=f(y) With x\geqslant 0. My initial thoughts were to take the Laplace transform in t...

Homework Statement 1) Determine the general solution of the equation 2) Use implict differentiation to verify that your solution satisfies the given PDE Homework Equations u u_x-y u_y=y The Attempt at a Solution \frac{dx}{u}=\frac{dy}{-y}=\frac{du}{y} Take the second two...

Greetings, I want to find the characteristics of the following parabolic PDE u_t + v u_x + w u_y + a(t, x,y,v,w, u) u_v + b(t, x,y,v,w, u) u_w - u_{vv} - u_{ww} = c(t,x,y,v,w,u) Where u=u(t,x,y,v,w) I know how to find the characteristics of a 2nd-order one-dimensional PDE. I also know how...

Hi, i'm having trouble finding a solution to this PDE, \frac{d U(x,y,t)}{dt} = A(x) \frac{\partial U(x,y,t)}{\partial y} + B(y) \frac{\partial U(x,y,t)}{\partial x} with only knowledge of the initial condition U(x,y,0)=F(x,y). I've tried to solve this using characteristics but the...

hi i can't make DSolve solve the wave equation with simple bvc ive gone through the mathematica documentation and can't find the answer for the input \text{DSolve}\left[\left\{u^{(2,0)}[x,t]==4 u^{(0,2)}[x,t],u[x,0]==1,u^{(0,1)}[x,0]==\text{Sin}[x]\right\},u,\{x,t\}\right] it just...

Homework Statement Sorry don't know how to use the partial symbol, bear with me partial u wrt t=2*(2nd partial u wrt x) Boundary conditions: partial u wrt x (0,t)=partial u wrt x (1,t)=0 Initial conditions u(x,0)=x(1-x) Homework Equations I get an answer that is different...

Hi everybody, I hope I am asking in the right forum. Let describe the problem as follows: I have a 1D heat equation. To solve it, I use finite-difference method to discretize the PDE and obtain a set of N ODEs. The larger N gives the better solution, i.e., the closer the solution to the...

Homework Statement \frac{\partial^2X}{\partial a^2} + (X^4-1)\frac{\partial X}{\partial a} = 0 Homework Equations How do I go about solving this PDE ? The Attempt at a Solution Please help !

Homework Statement 2\frac{\partial^2X}{\partial a \partial b} + \frac{\partial X}{\partial a}(x^4-1) = 0 Homework Equations How do I go about solving this PDE ?? The Attempt at a Solution Please help !

Homework Statement Solve This equation: \epsilon(Ut+Ux)+U=1 with \epsilon being a very small number from 0 to 1 and x bounds from neg infinity to pos infinity, t>0, and condition u(x,0)=sinxHomework Equations method of associated equation (dx/P=dt/Q=du/R, and so forth)The Attempt at a Solution...

For a general dynamic system: dXi/dt = Fi(X1, X2,...,Xn), i=1,...,n, Q.1 do you have some ideas of the existence conditions of following PDE: a) (grad U, grad U + F) = 0 in n-dimension domain, (,) is inner product; b) U >=0 Does it need a first type or second type of boundary...

I will love forever whoever can show me the steps of how to get the following equation in terms of y=[...] This is not a homework question. I have a calculus book that has given me some progress, such as expanding the equation to a mixture of terms and first order partial derivatives, and I...

PDE : Can not solve Helmholtz equation (This is not a homework. I doing my research on numerical boundary integral. I need the analytical solution to compare the results with my computer program. I try to solve this equation, but it not success. I need urgent help.) I working on anti-plane...

Hi This problem occurred on my final and I could not figure it out. Homework Statement The problem was a partial differential equation (I forgot the exact equation) but the solution was a hyperbolic function in the form of u(x,y)= f(x+y) + g (x+y), it was part b that gave me the...

Hi, Can anybody tell me the difference between a Cauchy Boundary condition and a combined Dirichlet/Neumann Boundary Condition for PDEs? The reason why I'm asking is because Cauchy boundary conditions can be used to solve Open Hyperbolic PDEs, whereas Dirichlet/Neumann can only be used to...

Homework Statement This is a simple pde I need to solve in order to determine a straightforward expansion for a given overall equation. Homework Equations \partialu/\partialx+\partialu/\partialy=0 with initial condition: u(x,0)=epsilon*phi(x) The Attempt at a Solution I...

Homework Statement Need to solve for dx/ds in the following equation, keeping dy/ds. Homework Equations d^2x/ds^2 - (2/y)(dx/ds)(dy/ds) = 0 The Attempt at a Solution I can just rearrange to get: dx/ds = (y/2)(ds/dy)(d^2x/ds^2) But, this is not clean to use for some later...

I just developed this model to describe an ecological process but have trouble solving the equation. My first question is: is the form even analytically solvable? And if so, what steps / references should I resort to? 'a', 'delta' and 'sigma' are all constants. *Current reference book...

I'm a theoretical biologist in the process of developing a spatial model for animal movement. So far, I've arrived at the following structure of an equation (see attachment): *theta is just some function of x and t. Having never formally studied pde, I'm wondering whether one can, from this...

Homework Statement I have Laplace's equation that I need to solve. I was told that it can be solved by separtion of variables and that it should yield sinh and cosh solutions. As it stands, my current set of BCs are not homogeneous. So I need to find the proper way to assume my solution...

have been solving PDEs by sep of variables, and the solution that comes out is generally a summation the general look of it is something like: U=SIGMA(n=1 to infinity)E_n(sin(n(pi)x/L)(cos(n)(pi)x/L)t The above may not be exactly right, I was thinking along the lines of heat equation where...

Problem: Use separation of variables to solve utt = uxx-u; u(x, 0) = 0; ut(x, 0) = 1 + cos3 x; on the interval (0, pi), with the homogeneous Dirichlet boundary conditions. Question: I know how to use separation of variables, but can`t figure out what to do with the u in the...

Hey, I want to solve a parabolic PDE with boundry conditions by using FINITE DIFFERENCE METHOD in fortran. (diffusion) See the attachment for the problem The problem is that there is a droplet on a leaf and it is diffusing in the leaf the boundry conditions are dc/dn= 0 at the upper...

Homework Statement Use separation of variables to find a general series solution of u_t + 4tu = u_{xx} for 0 < x < 1, t> 0 and u(0,t) = u(1,t)=0. Homework Equations The Attempt at a Solution Looking for a solution of the form u(x,t) = X(x)T(t) implies that \frac{T'}{kt} - \frac{X''}{X} = 0...

Hi, After considerable simplification in a problem I'm working on, I end up with the following partial differential equation: \partial_{\eta}\left(\frac{\sinh\eta}{\Delta}\partial_{\eta}g\right) + \partial_{\theta}\left(\frac{\sinh\eta}{\Delta}\partial_{\theta}g\right) + c^2\left[\frac{E_{p}...

Hi, I hope I posted in the right group. I read some papers about infinite dimensional systems and gave PDEs as examples of infinite dimensional systems. So far, I still cannot get why is that so. Could everybody here help me giving relation between a PDE and an infinite dimensional...

Homework Statement Solve the IVP for the wave equation: Utt-Uxx=0 for t>0 U=0 for t=0 Ut=[dirac(x+1)-dirac(x-1)] for t=0 2. The attempt at a solution By D' Almbert's solution: 1/2 integral [dirac(x+1)-dirac(x-1)] dx from (x-t) to (x+t) I apologize for not using Latex- my...

Homework Statement Show the two problems (i.e. give the boundary conditions and PDE's) that the given problem must be broken into in order to solve the PDE uxx+uyy=2u+f(x,y) satisfying the shown boundary conditions. Homework Equations See attachment. The Attempt at a Solution We...

Homework Statement As part of the solution to a HW problem of mine, I have to solve the PDE p_t = -vk^2 p - k \delta p_k, where p = p(k,t) and v,\delta are known constants. Homework Equations I tried to look for a solution of the form p(k,t) = K(k)T(t) and found one, but I'm not sure if I...

Hello physics enthusiasts! I was looking for resources, and stumbled upon these awesome forums. I am looking for how to solve the helmholtz equation / wave equation on a figure 8 type shape. I wanted to find the resonant frequencies of a classical guitar. Would this work? I am considering...