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# 偏微分方程课业代写 偏微分方程代写

2022-09-13 10:49 星期二 所属： 作业代写 浏览：41 ## Applied PDE – Homework Assignment 7:

Read, from Chapter 5.4 of Strauss – The Subsection entitled ”Three Notions of Convergence”; The Subsection entitled ”Convergence Theorems”, up to but not including Example 3;

Read, from Chapter 5.5 of Strauss – The first two paragraphs of the Subsection entitled ”The Gibbs Phenomena”;

Read, from Chapter 5.6 of Strauss – The first two pages, up to eq(10).

Homework: Chapter 5.4, problems 2, 8;

### Problem:   偏微分方程课业代写

Consider the ”Initial Boundary Value Problem” (IBVP) for the heat equation:

ut =νuxx,t >0,0< x < π,ν >0,

u(x,t= 0) =x2,

u(x= 0,t) = 0,

u(x=π,t) = 2.

i) Represent the solution as a Fourier Sine Series; ii) Compute the first two terms of the series explicitly; iii) What is the steady state or equilibrium solution?

### Problem:

Consider the ”Initial Boundary Value Problem” (IBVP) for the heat equation:

ut =νuxx,t >0,0< x < π,ν >0,

u(x,t= 0) =x2,

ux(x= 0,t) = 0,

ux(x=π,t) = 2.

i) Represent the solution as a Fourier Cosine Series; ii) Compute the first two terms of the series explicitly; iii) What is the steady state or equilibrium solution?

### Problem:  偏微分方程课业代写

Consider the (Neumann IBVP) for the inhomogeneous heat equation:

ut νuxx =f(x,t),t >0,0< x < π,

u(x,t= 0) =uin(x),

ux(x= 0,t) =ux(x=π,t) = 0. a (15 points): Construct the cosine series representation of the solution u(x,t) in three steps – i) Map the equation and data into Fourier space; ii) solve the initial value problem in Fourier space; iii) map the solution back to x-space. You can leave your answer in terms of integrals.

b (5 points): Consider the specific data

uin(x) =0

f(x,t) =δ(x1)exp(+t),

where δ(x1) is the Dirac delta function. For this specific data, do all of the integrals analytically. 