Hint: assume that there are two solutions u and v and consider a point on the boundary of D where u - v is maximal.
Homework Answers
Add Answer to:
Hint: assume that there are two solutions u and v and consider a point on the boundary of D where...
Prove that the following two-point boundary-value problem has a UNIQUE solution. Thank you Theorem on Unique Solution, Boundary-Value Problem Let f be a continuous function of (t, s), where 0stSl and...
Prove that the following two-point boundary-value problem has a
UNIQUE solution.
Thank you
Theorem on Unique Solution, Boundary-Value Problem Let f be a continuous function of (t, s), where 0stSl and-00<s< 00. Assume that on this domain THEOREM4 11. Prove that the following two-point boundary-value problem has a unique solution: "(t3 5)x +sin t
Theorem on Unique Solution, Boundary-Value Problem Let f be a continuous function of (t, s), where 0stSl and-00
please provide me with full working solution. Any help is appreciated. thank you in advance Consider the diffusion equation, au(x,t u(x,t) Here u(x,t) > 0 is the concentration of some diffusing...
please provide me with full working solution. Any help is
appreciated. thank you in advance
Consider the diffusion equation, au(x,t u(x,t) Here u(x,t) > 0 is the concentration of some diffusing substance, the spatial variable is x, time is t and D is a constant called the diffusivity with dimensions [LT-11. We will consider the diffusion equation on a finite spatial domain (0<x< 1) and an infinite time horizon (t > 0). To solve the diffusion equation we must include...
Problem 11. 12 marks] Consider the following two-point boundary value problem: y" + y' + ßy = 0, y(0) = 0, y(1) = 0, where ß is a real nurnber. we know the problern has a trivial solution...
Problem 11. 12 marks] Consider the following two-point boundary value problem: y" + y' + ßy = 0, y(0) = 0, y(1) = 0, where ß is a real nurnber. we know the problern has a trivial solution, i.e. y(x) = 0, Discuss how the value of B influences the nontrivial solutions of the boundary value problem, and get the nontrivial solutions (Find all the real eigenvalues β and the corresponding eigenfunctions.)
Problem 11. 12 marks] Consider the following two-point...
10. Prove the uniqueness of the Dirichlet problem Δι-f in D, 11-g on bdy D by...
10. Prove the uniqueness of the Dirichlet problem Δι-f in D, 11-g on bdy D by the energy method. That is, after subtracting two solutions w- u - v, multiply the Laplace equation for w by w itself and use the divergence theorem.
solve problem #1 depending on the given information Consider the following 1D second order elliptic equation with Dirichlet boundary conditions du(x) (c(x)du ) = f(x) (a $15 b), u(a) = ga, u(b) = gb...
solve problem #1 depending on the given information
Consider the following 1D second order elliptic equation with Dirichlet boundary conditions du(x) (c(x)du ) = f(x) (a $15 b), u(a) = ga, u(b) = gb dr: where u(x) is the unknown function, ga and gb are the Dirichlet boundary values, c(x) is a given coefficient function and f(x) is a given source function. See the theorem 10.1 in the textbook for the existence and uniqueness of the solution. 1.1 Weak Formulation...
Help would be greatly appreciated!! 1. Let S be the surface in R3 parametrized by the vector function ru, v)(,-v, v+ 2u) with domain D-{(u, u) : 0 u 1,0 u 2). This surface is a plane segment shaped...
Help would be greatly appreciated!!
1. Let S be the surface in R3 parametrized by the vector function ru, v)(,-v, v+ 2u) with domain D-{(u, u) : 0 u 1,0 u 2). This surface is a plane segment shaped like a parallelogram, and its boundary aS (with positive orientation) is made up of four line segments. Compute the line integral fos F -dr where F(z, y, z) = 〈エ2018 + y, 2r, r2-Ins). Hint: use Stokes' theorem to transform this...
Consider in x [0, L], the second order Boundary Value Problem lu where qra+bx. The solution is su...
Consider in x [0, L], the second order Boundary Value Problem lu where qra+bx. The solution is subject to the boundary conditions du dxl Find an approximate solution using the using a three-node element. The shape function of the element is, in a local coordinate system s E[, Thus local node number 1 is to the left (s--1) and number 2 is in centre (s -0) and the third node is to the right (s 1) Hint: Assume that the...
1 point) Show that Φ(u, u) (Au + 2, u-u, 7u + u) parametrizes the plane 2x -y-z = 4, Then (a) Calculate Tu T,, and n(u, v). þ(D), where D = (u, u) : 0 < u < 9,0 < u < 3. (b) Find the area...
1 point) Show that Φ(u, u) (Au + 2, u-u, 7u + u) parametrizes the plane 2x -y-z = 4, Then (a) Calculate Tu T,, and n(u, v). þ(D), where D = (u, u) : 0 < u < 9,0 < u < 3. (b) Find the area of S (c) Express f(x, y, z in terms of u and v and evaluate Is f(x, y,z) ds. (a) Tu n(u,v)- T, (b) Area(S)- (c) JIs f(z, y,2) ds-
1 point)...
Slove 4.3.8 please axbycz d be the equation of a plane with normal Exercise 4.3.16 a. Show that w- (u x v) = u (vxw) = v...
Slove 4.3.8
please
axbycz d be the equation of a plane with normal Exercise 4.3.16 a. Show that w- (u x v) = u (vxw) = v x (w x u) holds for all vectors w, u, and v. n= C w and (u x v) + (vxw) +(wxu) b. Show that v- a. Show that the point on the plane closest to Po has vector p given by are orthogonal Exercise 4.3.17 Show u x (vxw) = (u w)v-...
In a steady-state two-dimensional heat flow problem, the temperature, u, at any point in the doma...
In a steady-state two-dimensional heat flow problem, the temperature, u, at any point in the domain (x, y) satisfies the following differential equation. With the given temperature boundary condition, find the internal temperature at points a, b, and c using a numerical method. 0 4 4
In a steady-state two-dimensional heat flow problem, the temperature, u, at any point in the domain (x, y) satisfies the following differential equation. With the given temperature boundary condition, find the internal temperature at...
Prove that the following two-point boundary-value problem has a
UNIQUE solution.
Thank you
Theorem on Unique Solution, Boundary-Value Problem Let f be a continuous function of (t, s), where 0stSl and-00<s< 00. Assume that on this domain THEOREM4 11. Prove that the following two-point boundary-value problem has a unique solution: "(t3 5)x +sin t
Theorem on Unique Solution, Boundary-Value Problem Let f be a continuous function of (t, s), where 0stSl and-00
please provide me with full working solution. Any help is
appreciated. thank you in advance
Consider the diffusion equation, au(x,t u(x,t) Here u(x,t) > 0 is the concentration of some diffusing substance, the spatial variable is x, time is t and D is a constant called the diffusivity with dimensions [LT-11. We will consider the diffusion equation on a finite spatial domain (0<x< 1) and an infinite time horizon (t > 0). To solve the diffusion equation we must include...
Problem 11. 12 marks] Consider the following two-point boundary value problem: y" + y' + ßy = 0, y(0) = 0, y(1) = 0, where ß is a real nurnber. we know the problern has a trivial solution, i.e. y(x) = 0, Discuss how the value of B influences the nontrivial solutions of the boundary value problem, and get the nontrivial solutions (Find all the real eigenvalues β and the corresponding eigenfunctions.)
Problem 11. 12 marks] Consider the following two-point...
10. Prove the uniqueness of the Dirichlet problem Δι-f in D, 11-g on bdy D by the energy method. That is, after subtracting two solutions w- u - v, multiply the Laplace equation for w by w itself and use the divergence theorem.
solve problem #1 depending on the given information
Consider the following 1D second order elliptic equation with Dirichlet boundary conditions du(x) (c(x)du ) = f(x) (a $15 b), u(a) = ga, u(b) = gb dr: where u(x) is the unknown function, ga and gb are the Dirichlet boundary values, c(x) is a given coefficient function and f(x) is a given source function. See the theorem 10.1 in the textbook for the existence and uniqueness of the solution. 1.1 Weak Formulation...
Help would be greatly appreciated!!
1. Let S be the surface in R3 parametrized by the vector function ru, v)(,-v, v+ 2u) with domain D-{(u, u) : 0 u 1,0 u 2). This surface is a plane segment shaped like a parallelogram, and its boundary aS (with positive orientation) is made up of four line segments. Compute the line integral fos F -dr where F(z, y, z) = 〈エ2018 + y, 2r, r2-Ins). Hint: use Stokes' theorem to transform this...
Consider in x [0, L], the second order Boundary Value Problem lu where qra+bx. The solution is subject to the boundary conditions du dxl Find an approximate solution using the using a three-node element. The shape function of the element is, in a local coordinate system s E[, Thus local node number 1 is to the left (s--1) and number 2 is in centre (s -0) and the third node is to the right (s 1) Hint: Assume that the...
1 point) Show that Φ(u, u) (Au + 2, u-u, 7u + u) parametrizes the plane 2x -y-z = 4, Then (a) Calculate Tu T,, and n(u, v). þ(D), where D = (u, u) : 0 < u < 9,0 < u < 3. (b) Find the area of S (c) Express f(x, y, z in terms of u and v and evaluate Is f(x, y,z) ds. (a) Tu n(u,v)- T, (b) Area(S)- (c) JIs f(z, y,2) ds-
1 point)...
Slove 4.3.8
please
axbycz d be the equation of a plane with normal Exercise 4.3.16 a. Show that w- (u x v) = u (vxw) = v x (w x u) holds for all vectors w, u, and v. n= C w and (u x v) + (vxw) +(wxu) b. Show that v- a. Show that the point on the plane closest to Po has vector p given by are orthogonal Exercise 4.3.17 Show u x (vxw) = (u w)v-...
In a steady-state two-dimensional heat flow problem, the temperature, u, at any point in the domain (x, y) satisfies the following differential equation. With the given temperature boundary condition, find the internal temperature at points a, b, and c using a numerical method. 0 4 4
In a steady-state two-dimensional heat flow problem, the temperature, u, at any point in the domain (x, y) satisfies the following differential equation. With the given temperature boundary condition, find the internal temperature at...
Most questions answered within 3 hours.
-
You purchase your daily coffee at the Chemist’s Coffeehouse and
have a choice of two cups:...
asked 2 hours ago -
Which of the following pairs of chemicals could be used to make
a buffer solution?
A.)...
asked 1 hour ago -
Problem 16-51 Sales
Activity Variance (LO 16-3)Odessa, Inc., reports the following
information concerning operations for the...
asked 2 hours ago -
Pictured on the right are thee point charges Q1 = 18.4 μC, Q2 =
-30.6 μC,...
asked 2 hours ago -
A graduate student is conducting research in psychology and
needs to obtain the IQ scores of...
asked 3 hours ago -
R2.84: There are 2 defective products in a production lot of 10.
An inspector randomly selected...
asked 4 hours ago -
Consider the following equilibrium system: COCl2(g) CO(g) +
Cl2(g) A 10.00 L evacuated flask is filled...
asked 4 hours ago -
1) What are the two distinct steps that one needs to perform
when developing a data...
asked 5 hours ago -
2) Write a C++ program that uses a class called “Degree” to
obtain the trigonometric
values...
asked 6 hours ago -
1. In eukaryotic cells the genomes of
&
asked 6 hours ago -
The standard enthalpy of propanol (C3H7OH) is -303.0 kJ/mol.
Compute both of the
gross and net...
asked 6 hours ago -
Why PWM using H-bridge for control motor speed is more power
effiecient than the linear amplifier...
asked 6 hours ago