Let u (x) be the equilibrium solution to the Dirich let boundary value problem for a bar k u f, u,() u () 0 Prove that if f(x) 0 then the total energy at equilibrium is strictly negative p u 0 ...

According to 119192 or using a direct integr ...

Let u.(x) be the equilibrium solution to the Dirich- let boundary value problem for a bar: k[u.]

Question:

Let u.(x) be the equilibrium solution to the Dirich- let boundary value problem for a bar: k[u.] = f, u,(ℓ) = u.(ℓ) = 0. Prove that if f(x) = 0. then the total energy at equilibrium is strictly negative: p[u.] < 0.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

See More Books

Question Posted: Jun 18, 2016 09:07 AM

See More Questions

Let , c be fixed. Solve the affine (or inhomogeneous linear) iterative equation u(k+l) = u(k) + c, u(0) = a. (10.5) Discuss the possible behaviors of the solutions. Write the solution in the form...
Let a be complex. Prove that u(t) = ceat is the (complex) solution to our scalar ordinary differential equation (8.1). Describe the asymptotic behavior of the solution as t , and the stability...
Let A be a constant n x n matrix, and suppose u(t) is a solution to the system (a) Show that all derivatives dku/dtk k = 1, 2....... are also solutions. (b) Show that 4-A dt d'u LI =Atu. dtk
On July 31, 2019, the balances of the accounts appearing in the ledger of Serbian Interiors Company, a furniture wholesaler, are as follows: Prepare the July 31, 2019, closing entries for Serbian...
What forces have led to the boom in entrepreneurship in the United States?
Explain the case library development process.
16. Do you have any other comments or suggestions?
You anticipate buying a Volvo in six months for $30,000. Currently the spot price of the Swedish krona is $0.50 and the six-month futures price is $0.505. You anticipate that the value of the dollar...
The following information is for the inventory of mini-kettles at Whispering Winds Company Limited for the month of May. Date Transaction Units In Unit Cost Total Units Sold Unit Price Total May 1...
Allie has bought a new apple orchard. The orchard has a single file of trees, numbered from 1 to N. Each tree has a certail number of ripe apples. Allie has a rule she wants to follow. She wants to...
Show that the internal energy in a bar (the first term in (11.92)) is one half the unweighted L2 inner product between stress and strain: 1/2 ||D[u||2 = l/2(v, w).
When possible, find and graph the displacement u(x) and bending moment w(x) of a beam of unit length l = 1 with constant bending stiffness c(x) = 1 subject to a unit gravitational force when it has...
Verify the standard errors reported in Eq. (20.5.3).
15.5 please help will give like if answers r correct Exercise 15-8 (Static) Sales-type lease with selling profit; lessor; calculate lease payments [LO15-3] Manufacturers Southern leased high-tech...
When my son was young, he had 8 different plastic dinosaurs to arrange. How many ways could he arrange his 8 dinos? He had favorite dinos, so placing them in proper order was very important. How many...
Process P1 init (mutEx); num = 0; loop1 = 0; while (loop1 < 3) wait (mutEx); num num + 1; signal (mutEX); loop1 loop1 + 1; Process P2 loop2 = 0; while (loop2 < 2) wait (mutEx); num num + 10;...
PROBLEM 3-5B Following is the chart of accounts of Smith Financial Services: Assets 111 Cash 113 Accounts Receivable 115 Supplies 117 Prepaid Insurance 124 Office Furniture Liabilities 221 Accounts...
4. Identify a service you could refer Casey to and write a referral for her (up to 300 words).
Let (x) = x 5 + x 2 . The secant line between (0, 0) and (1, 2) has slope 2 (check this), so by the MVT, '(c) = 2 for some c (0, 1). Plot f and the secant line on the same axes. Then plot y = 2x + b...
Annual dividends of ATTA Corp grew from $0.96 in 2005 to $1.76 in 2017. What was the annual growth rate?
A radar gun was used to record the speed of a runner at the times given in the table. Use the Midpoint Rule to estimate the distance the runner covered during those 5 seconds. e (m/s) P (m/s) I (s)...
A population of honeybees increased at a rate of r(t) bees per week, where the graph of r is as shown. Use the Midpoint Rule with six subintervals to estimate the increase in the bee population...
If x sin x = x2 f(t) dt, where f is a continuous function, find f(4).
What is Apple Companys strategy for success in the marketplace? Does the company rely primarily on customer intimacy, operational excellence, or product leadership? What evidence supports your...
Exercise 1 1 - 7 ( Algo ) Net present value and unequal cash flows LO P 3 Gomez is considering a $ 2 1 0 , 0 0 0 investment with the following net cash flows. Gomez requires a 1 2 % return on its...
a Campbell Inc. produces and sells outdoor equipment. On July 1, 2011. Campbell issued $40,000,000 a 10-year, 10% bonds at a market (effective) interest rate of 9%, receiving Cash of 548,601,480....

Let u.(x) be the equilibrium solution to the Dirich- let boundary value problem for a bar: k[u.]

Question:

Step by Step Answer:

According to 119192 or using a direct integr...View the full answer

Applied Linear Algebra

Students also viewed these Linear Algebra questions