Quasi-Linear Partial Differential Equation
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Initial Value Problem and Method of Characteristics
Solve the following initial data problem: u_x + u_y = u^2 u(x,0) = h(x) I have that x_t = 1, y_t = 1 and z_t = z^2 also, x(0) = s, y(0) = 0 and z(0)=h(s) from this I have x=s + t and y=t Please provide a detailed solution of how to find z.
Partial Differential Equation : Method of Characteristics
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Show that exp(x) is not a tempered distribution. Please justify your steps. Thank you
Compute the 1-dimensional FT of 1/(1+x^2)^k by applying the calculus of residues.
Partial Differential Equations : Solve the 1st order linear equation.
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Convergent Power Series and Heat Equation
Show that there always exist a convergent power series solution to the heat equation with u(x,0)=p(x)=polynomial. Is the solution a polynomial?
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Solving Partial Differential Equations by Change of Variables and Characteristic Curves
In solving this problem, derive the general solution of the given equation by using an appropriate change of variables. 1. ∂u/∂t – 2 ∂u/∂x = 2 Answer: u(x,t) = f(x + 2t) – x In this exercise, (a) solve the given equation by the method of characteristic curves, and (b) check you answer by plug ...continues
Partial Differential Equations : Burgers' Equation
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