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Consider the inlínitm ar ls sby subject to the initial conditions u(x,0)-f() and u(,0)-9(x) where 0, otherwise (a) What is the wave speed? c (b) What is the domain of dependence for the point (r, t)...
9. Solve the wave equation subject to the boundary and initial conditions u(0,t) = 0, u(x,0)...
9. Solve the wave equation subject to the boundary and initial conditions u(0,t) = 0, u(x,0) = 0, U(TT, t) = 0, t> 0 $ (3,0) = sin(x), 0<x<a
r Extra Credit: Write a complete analysis of the wave equation with friction for a string of length L subject to initial conditions u(x, 0)-f(x) and (x,0) (t) r Extra Credit: Write a complete...
r Extra Credit: Write a complete analysis of the wave equation with friction for a string of length L subject to initial conditions u(x, 0)-f(x) and (x,0) (t)
r Extra Credit: Write a complete analysis of the wave equation with friction for a string of length L subject to initial conditions u(x, 0)-f(x) and (x,0) (t)
(1 point) Consider the wave equation 1(1)utt = uzz for-oo < z < oo, t>0 with initial conditions ut (z,0-0 and u(z,0) = /(z), where (2) f(z) = 1 for 0 < z < 1, (3) f(z) =...
(1 point) Consider the wave equation 1(1)utt = uzz for-oo < z < oo, t>0 with initial conditions ut (z,0-0 and u(z,0) = /(z), where (2) f(z) = 1 for 0 < z < 1, (3) f(z) =-1 for-1 < z < 0, and (4) f(z) = 0 for all other. The slanting lines in the figure below show the characteristics for this PDE that originate on the z-axis at the points of discontinuity of the initial data f f(x)...
Problem 1. Consider the nonhomogeneous heat equation for u(r, t) subject to the nonhomogenoous boundary conditions u(0, t) 1, u(r, t) 0, t>o and the initial condition u(, 0)in() Find the solut...
Problem 1. Consider the nonhomogeneous heat equation for u(r, t) subject to the nonhomogenoous boundary conditions u(0, t) 1, u(r, t) 0, t>o and the initial condition u(, 0)in() Find the solution u (z, t) by completing each of the following steps: (a) Find the equilibrium temperature distribution t) (b) Den ote u(x, t)-u(x, t)-ue(x). Derive the IBVP for the function u(x,t). (c) Find v(x, t) (d) Find u(x,t)
Problem 1. Consider the nonhomogeneous heat equation for u(r, t) subject...
Problem 1. Consider the nonhomogeneous heat equation for u(,) subject to the nonhomogeneous boundary conditions 14(0,t) 1, u(r,t)-0,t> and the initial condition the solution u(x, t) by complet...
Problem 1. Consider the nonhomogeneous heat equation for u(,) subject to the nonhomogeneous boundary conditions 14(0,t) 1, u(r,t)-0,t> and the initial condition the solution u(x, t) by completing each of the following steps (a) Find the equilibrium temperature distribution u ( (b) Denote v, t)t) - u(). Derive the IBVP for the function vz,t). (c) Find v(x, t) (d) Find u(x, t)
Problem 1. Consider the nonhomogeneous heat equation for u(,) subject to the nonhomogeneous boundary conditions 14(0,t) 1, u(r,t)-0,t>...
please show work i will rate you Extra Credit: Write a complete analysis of the wave equation with friction for a string of length L subject to initial conditions u(x,0) = f(x) and 쓿(x,0) = g(t)....
please show work i will rate you
Extra Credit: Write a complete analysis of the wave equation with friction for a string of length L subject to initial conditions u(x,0) = f(x) and 쓿(x,0) = g(t).
Extra Credit: Write a complete analysis of the wave equation with friction for a string of length L subject to initial conditions u(x,0) = f(x) and 쓿(x,0) = g(t).
7.17 (a) Solve the equation u, 2u, in the domain 0< x<T, t>0 under the initial...
7.17 (a) Solve the equation u, 2u, in the domain 0< x<T, t>0 under the initial boundary value conditions u(0,t)= u(r, t) 0, u(x, 0) = f(x) = x(x2 -n2). (b) Use the maximum principle to prove that the solution in (a) is a classical solution. 7.18 Prove that the formulas (7.72)-(7.75) describe solutions of (7.70)-(7.71) that are
7.17 (a) Solve the equation u, 2u, in the domain 0
au du atua = 90, дх with the initial conditions at t = 0: u=0 if...
au du atua = 90, дх with the initial conditions at t = 0: u=0 if u=-1-1 u=1 - << -1, if -1 <I<0, if 0 < I< 0. (Define u(r, t), x,t and the constant qo appropriately.) (b) Use the method of characteristics along suitable curves r(t) to obtain the implicit equation satisfied by the general solution ur,t) of the PDE given in the first problem (do not have to use the initial conditions at this stage, so there...
For 0 x π , 0S9, π , and 120 , solve the 2-D wave equation subject to the following conditions. u(0,y,t)-0, u(T.yt):0, u(x,0,) u(x,π, t) 0, 0 Boundary condition: C11 1 u(x),0)-sin(x)sin(2y) + sin(2x)...
For 0 x π , 0S9, π , and 120 , solve the 2-D wave equation subject to the following conditions. u(0,y,t)-0, u(T.yt):0, u(x,0,) u(x,π, t) 0, 0 Boundary condition: C11 1 u(x),0)-sin(x)sin(2y) + sin(2x)sin(4y), 0 at It=0 Initial condition:
For 0 x π , 0S9, π , and 120 , solve the 2-D wave equation subject to the following conditions. u(0,y,t)-0, u(T.yt):0, u(x,0,) u(x,π, t) 0, 0 Boundary condition: C11 1 u(x),0)-sin(x)sin(2y) + sin(2x)sin(4y), 0 at It=0 Initial condition:
3. [4] The solution of the wave equation02, which satisfies the boundary conditions u(0,t) = u(2,...
3. [4] The solution of the wave equation02, which satisfies the boundary conditions u(0,t) = u(2,t) 0, is given by a cos+b sin If u(, t) satisfies the initial conditions u(x, 0)-0 and u(x,0)3sin(Tx) - sin(3T), find the coefficients an and bn Solution: b2 = , bs =- π 97T bn-0 otherwise, and an - 0 for all n 21.
3. [4] The solution of the wave equation02, which satisfies the boundary conditions u(0,t) = u(2,t) 0, is given by...
9. Solve the wave equation subject to the boundary and initial conditions u(0,t) = 0, u(x,0) = 0, U(TT, t) = 0, t> 0 $ (3,0) = sin(x), 0<x<a
r Extra Credit: Write a complete analysis of the wave equation with friction for a string of length L subject to initial conditions u(x, 0)-f(x) and (x,0) (t)
r Extra Credit: Write a complete analysis of the wave equation with friction for a string of length L subject to initial conditions u(x, 0)-f(x) and (x,0) (t)
(1 point) Consider the wave equation 1(1)utt = uzz for-oo < z < oo, t>0 with initial conditions ut (z,0-0 and u(z,0) = /(z), where (2) f(z) = 1 for 0 < z < 1, (3) f(z) =-1 for-1 < z < 0, and (4) f(z) = 0 for all other. The slanting lines in the figure below show the characteristics for this PDE that originate on the z-axis at the points of discontinuity of the initial data f f(x)...
Problem 1. Consider the nonhomogeneous heat equation for u(r, t) subject to the nonhomogenoous boundary conditions u(0, t) 1, u(r, t) 0, t>o and the initial condition u(, 0)in() Find the solution u (z, t) by completing each of the following steps: (a) Find the equilibrium temperature distribution t) (b) Den ote u(x, t)-u(x, t)-ue(x). Derive the IBVP for the function u(x,t). (c) Find v(x, t) (d) Find u(x,t)
Problem 1. Consider the nonhomogeneous heat equation for u(r, t) subject...
Problem 1. Consider the nonhomogeneous heat equation for u(,) subject to the nonhomogeneous boundary conditions 14(0,t) 1, u(r,t)-0,t> and the initial condition the solution u(x, t) by completing each of the following steps (a) Find the equilibrium temperature distribution u ( (b) Denote v, t)t) - u(). Derive the IBVP for the function vz,t). (c) Find v(x, t) (d) Find u(x, t)
Problem 1. Consider the nonhomogeneous heat equation for u(,) subject to the nonhomogeneous boundary conditions 14(0,t) 1, u(r,t)-0,t>...
please show work i will rate you
Extra Credit: Write a complete analysis of the wave equation with friction for a string of length L subject to initial conditions u(x,0) = f(x) and 쓿(x,0) = g(t).
Extra Credit: Write a complete analysis of the wave equation with friction for a string of length L subject to initial conditions u(x,0) = f(x) and 쓿(x,0) = g(t).
7.17 (a) Solve the equation u, 2u, in the domain 0< x<T, t>0 under the initial boundary value conditions u(0,t)= u(r, t) 0, u(x, 0) = f(x) = x(x2 -n2). (b) Use the maximum principle to prove that the solution in (a) is a classical solution. 7.18 Prove that the formulas (7.72)-(7.75) describe solutions of (7.70)-(7.71) that are
7.17 (a) Solve the equation u, 2u, in the domain 0
au du atua = 90, дх with the initial conditions at t = 0: u=0 if u=-1-1 u=1 - << -1, if -1 <I<0, if 0 < I< 0. (Define u(r, t), x,t and the constant qo appropriately.) (b) Use the method of characteristics along suitable curves r(t) to obtain the implicit equation satisfied by the general solution ur,t) of the PDE given in the first problem (do not have to use the initial conditions at this stage, so there...
For 0 x π , 0S9, π , and 120 , solve the 2-D wave equation subject to the following conditions. u(0,y,t)-0, u(T.yt):0, u(x,0,) u(x,π, t) 0, 0 Boundary condition: C11 1 u(x),0)-sin(x)sin(2y) + sin(2x)sin(4y), 0 at It=0 Initial condition:
For 0 x π , 0S9, π , and 120 , solve the 2-D wave equation subject to the following conditions. u(0,y,t)-0, u(T.yt):0, u(x,0,) u(x,π, t) 0, 0 Boundary condition: C11 1 u(x),0)-sin(x)sin(2y) + sin(2x)sin(4y), 0 at It=0 Initial condition:
3. [4] The solution of the wave equation02, which satisfies the boundary conditions u(0,t) = u(2,t) 0, is given by a cos+b sin If u(, t) satisfies the initial conditions u(x, 0)-0 and u(x,0)3sin(Tx) - sin(3T), find the coefficients an and bn Solution: b2 = , bs =- π 97T bn-0 otherwise, and an - 0 for all n 21.
3. [4] The solution of the wave equation02, which satisfies the boundary conditions u(0,t) = u(2,t) 0, is given by...
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