Questions tagged [characteristics]

The method of characteristics is a way of solving certain partial differential equations by reducing them to ordinary differential equations. It is most often used for 1st order equations. Use with the (pde) tag.

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Hard Partial Differential Equations - Characteristics

$$(x-y)\frac{\partial u}{\partial x}+(x+y)\frac{\partial u}{\partial y}=\alpha u$$ where α is a constant, with initial condition $u(x, 0) = x^2$ , $x > 0$. How do I solve this partial ...
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Triple-valued solution to Riemann problem - Profile of the bulge

I am studying conservation laws and hyperbolic systems, particularly, Burgers' equation and shocks, and have a doubt at pages 48/49 of the book Numerical Methods for Conservation Laws by R.J. LeVeque (...
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Method of characteristics PDE $u_t +uu_x = x$

In this question you are asked to solve the initial value problem \begin{aligned} u_t +uu_x &= x,\\ u(x, 0) &= f(x) \end{aligned} using the method of characteristics. Using the parameters $s$ ...
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Entropy solution to inviscid Burgers with triangular initial data

Find the entropy solution of $$\begin{cases} u_t + \left( \frac{u^2}{2} \right)_x = 0 & \text{ in } \mathbb{R}\times(0,\infty) \\ u = g & \text{ on } \mathbb{R}\times\{0\}, \end{cases}$$ ...
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$u_t+[u(1-u)]_x=0$ with initial conditions - Need help with rarefaction wave portion
I need help solving $$u_t+[u(1-u)]_x=0$$ with initial conditions $$u(x,0) = \begin{cases} 0.75 & |x|<0.5\\ 0 & else \end{cases}$$ I am trying to use the method of characteristics but I am ...