Pde Definition and 856 Threads

I'm trying to solve equation in the attached pdf, which describes anistropic diffusion in 3D with an additional term to account for hydrogen bonding and unbonding of the diffusing substance to the medium. I've considered Laplace transforms, then solving in the Laplace domain, then inverting...

How to solve this nonlinear PDE? Please help! Hello Everyone, I am trying to solve the following nonlinear PDE which is driven from the Hamilton Jacobi Bellman (HJB) equation in ergodic control of a nonlinear dynamical system. v\nabla_x h - \frac{1}{4}\|\nabla_v h\|^2 + \frac{1}{2} \sigma...

Im a rising junior in the US starting my upper division physics classes. I have an opening this quarter and want to take an applied math course, but cannot decide between these two: In the mathematics department: "Applied complex anlysis Introduction to complex functions and their applications...

Hello: I am wondering if there is a general way of splitting the following PDE into two separate equations. I would like to re-write the second-order spatial derivatives on the LHS as first-order derivatives. \[ \frac{{\partial p^2 }}{{\partial x^2 }} + \frac{{\partial p^2 }}{{\partial...

find the general solution of yux+xuy=yu+xex ( the solution is in the form of u(x,y)=yex+f(y2-x2)ex ) if at first the value of u(x,y) on the upper half of hyperbola (that is y>=1) has been given as φ,show that if φ has not been given as a special form there is no solution.find that special form...

Hello all! I appreciate it if you can share any thoughts that you may have regarding how to solve the following PDE: \frac{\partial U(z,t)}{\partial t}+(1-z)\frac{\partial U(z,t)}{\partial z}=(\frac{1}{z}-1)\left(U(z,t)-U(0,t)\right) Initial condition:U(z,0)=z^{K} U(0,t) arises due...

Hi All, For one of my courses this year (a mathematical modeling course) we have been given a very open ended assignment to go and find some PDE describing ANYTHING in the literature that has an analytical solution and basically go through the solution step by step and present it/explain it...

Homework Statement Transform to normal form and solve: 1) u_{xx}+u_{xy}-2u_{yy} = 0Homework Equations Normal form: Au_{xx}+2Bu_{xy}+Cu_{yy}, hence, A = 1, B = \frac{1}{2}, C = -2. Since AC-B^2 = -2.25 < 0 this is a hyperbolic equation. Want to transform it by setting v = \Phi(x,y), z =...

Why is the characteristic of (d/dx) + (d/dt) = 0 where d is small delta c = x - t and not c = x + t

I have the following equation to solve: u_{tt}=12{u_x}^2+12u_{xx}+{u_x}^4+6u_{xx}{u_x}^2+4u_{xxx}u_x+3{u_{xx}}^2+u_{xxxx} I have been told to look into FDM or FEM. My question, is it possible to code something in MATLAB to solve this and if so what is the best method to use and how do I do...

Homework Statement how can i solve this problem by MATLAB? pls help me A (d4y/dx4) - B(d2y/dt2) = Cy A=E*I B=p*sin(w*t) c=p*w2 conditions are 1.at x=0, dy/dx=0 2.at x=0,y=0 3.at x=L d2y/dx2=0 4. at x=L d3y/dx3=p (p is a function of t here) x=0 and x=L...

Homework Statement I have the damped wave equation; u_{tt} = 4 u_{xx} -2 u_{t} which is to be solved on region 0 < x < 2 with boundary conditions; u(0,t) = 2, u(2,t) = 1. i must; 1) find steady state solution u_{steady}(x) and apply boundary conditions. 2) find \theta(x,t)...

Homework Statement Question attached Homework Equations The Attempt at a Solution I'm mostly wondering with c) and also want to check if my solution is correct. My solutions for this question are: u(x,t)= -1/2 for x <= -1/2*t = 1 for -t < x < 1-t = 1/2 for x =>...

Hi. I'm following the solution of a Klein-Gordon PDE in a textbook. The equation is \begin{align} k_{xx}(x,y) - k_{yy}(x,y) &= \lambda k(x,y) \\ k(x,0) &= 0 \\ k(x,x) &= - \frac{\lambda}{2} x \end{align} The book uses a change of variables $\xi = x+y$, $\eta = x-y$ to write \begin{align}...

I need to solve the following system of differential equations: \frac{\partial^2 y}{\partial t^2} + A\frac{\partial y}{\partial t} - B \frac{\partial^2 y}{\partial z^2} = Cq \frac{\partial^2 q}{\partial t^2} + D\frac{\partial q}{\partial t} + q = E\frac{\partial^2 y}{\partial t^2}...

I'm trying to solve this equation: Ux + Uy + U = e^-(x+y) with the initial condition that U(x,0)=0 I played around and and quickly found that U = -e^-(x+y) solves the equation, but does not hold for the initial condition. For the initial condition to hold, I think there needs to be some...

I need to know some of the application of partial differential equation in mechanic ? just need some headlines and I 'll Google them . thanks

Dear Mathematicians and Physicists, In light of the coming fall semester, I am having a decision to take a full blown graduate level Elliptic PDE class. The prerequisites is of course Graduate level analysis and perhaps a undergrad class in PDE, both of which I already have. The class will be...

Dear all, I'm trying to solve the 2d heat equation in a radially symmetric domain, numerically using the Crank-Nicolson method. i.e. \dfrac{\partial u}{\partial t} = D\left( \dfrac{\partial^2u}{\partial r^2}+\dfrac{1}{r}\dfrac{\partial u}{\partial r}\right) Applying the Crank-Nicolson...

Hi, I have this problem, I need to plot the solution of the next nonlinear-PDE problem: y_{tt}=((y_x)^3)_x+y^3-y where y=y(x,t), and we are looking for a solution with a compact support in (-x0,x0) (which I need to find x0), i.e the solution vanishes for x>=x0 or x<=-x0, and also y=y_x=0 on...

Homework Statement δu/δt+2tδu/δx=1 for t>0,x>0 with u= 0 on x= 0 for t>0, u=1 at t=0 for x≥0 Homework Equations The Attempt at a Solution ((dx)/(dt))=2t x=t²+c x-t²=c the general solution is: u=t+F(x-t²) Now i am...

From PDE to ODE ?! + research Homework Statement In the attached research, What are the steps that we work to transform the equation (1) to (8) Homework Equations (1) and (8) The Attempt at a Solution I know that they used similarity transformations but I do not know how to do...

I am a senior in mathematics studying graduate point-set topoology atm. I am thinking I want to study differential topology in graduate school and maybe apply it to problems in cosmology. Do I need to take more ODE and PDE? I took intro to diff eq- the one that all engineering undergrads take...

I'm following an algorithm my teacher gave us and I'm trying to understand it... I'm trying to solve this PDE 2Ux-Uy+5U=10 with U(x,0)=0 First I need to solve the homogeneous equation. So I set up the relation: V(y)=U(2y+c, y) to solve 2Ux-Uy=0 where the characteristic equation is y=1x/2...

I'm working on a problem in multi-allele diffusion in population genetics and I have come to this PDE: 0 = (tp_1(1-p_1)-sp_2)\frac{\partial u}{\partial p_1}+(sp_2(1-p_2)-tp_1)\frac{\partial u}{\partial p_2} + \frac{p_1(1-p_1)}{2}\frac{\partial^2 u}{\partial p_1^2} +...

Hey guys, I'm having a little difficulty with a pde I'm trying to solve. It boils down to solving for a first integral. I don't want the answer, but I'd be glad to get a little help. We have the system: \frac{dx}{x^2} = \frac{dy}{y^2} = \frac{dz}{xy(z^2 + 1)} We can use the first two and find...

Dear all, I'm trying to solve the diffusion PDE for my system, shown below: \frac{\partial C}{\partial t} = D (\frac{\partial^2 C}{\partial r^2} + \frac{1}{r} \frac{\partial C}{\partial r}) where C is the concentration, changing with time t and radius r. D is the diffusion...

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...

Hi there, could anyone help me on this particularly frustrating problem I am having... I have a linear parabolic homogeneous PDE in two variables with a boundary condition that is a piecewise function. I can solve the pde (with a homogeneous BC) however trying to impose the actual BC makes...

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 am trying to solve (1) U_t = 2bU_xy (as part of U_t = aU_xx + 2bU_xy + cU_yy) using centred finite difference method. When a > 0 everyhing is OK but when a < 0 I get some oscillation problems. My questions are: 1. is there a pde theory for (1)? 2. what is the 'motivation' for (1)...

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) 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} The...

Homework Statement I need to solve the Eikonal Equation c^2(u_x^2 + u_y^2) = 1 Initial condition u(x,0) = 0 C(x,y) = |x|, but x>0 to essentially C = x Oh. And the solution is given as \ln{\frac{\sqrt{x^2 + y^2} + y}{x}} Homework Equations None other than the usual method of...

Somie info about this PDE please ?? \frac{\partial u}{\partial t} = r u - (1+\nabla^2)^2u + f(u) where f(u) is an smooth function , u=U(x,t) is the solution of the PDE this is the Swift-Hohenberg equation, my teacher has asked me to solve it or look some info about it specially -...

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 The 2d PDE Assume f\in S(\mathbb{R}^2) (Schwartz space) Then solve u_{xx}(x,y) + 2u_{yy}(x,y) + 3u_{x}(x,y) -4u(x,y) = f(x,y) ; (x,y) \in\mathbb{R}^2 u_{xxxx}(x,y) - u_{yy}(x,y) + 2u(x,y) = f(x,y) ; (x,y) \in\mathbb{R}^2 Homework Equations The relevant...

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 all, I'm a graduate student of engineering and have some knowledge of solving ODEs and PDEs - usually enough to do the simulations I need. However, I'm currently stumped by a PDE I found in a paper. I've attached the PDE in question (the Herring-Trilling equation) to this post. I'm...

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...

I'm looking to delve into PDEs. I'm reading thru Lee's Smooth Manifolds, and he has a chapter on integral manifolds, and how they relate to PDE solutions via Frobenius' theorem. I find the hint of geometrical aspects very appealing. Evans' PDE book (that I was planning on picking up)...