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Last active June 20, 2017 09:53
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Nonlinear PDE
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pdedescription.md

Hi, I'm trying to solve a nonlinear PDE that looks similar to a time-dependent eikonal equation. Can anyone provide me some advise for the best Julia-ecosystem approach to solving it, please?

I'm trying to find $$v:[0,1]\times \mathbb R_{\geq 0}^2$$, such that $$ v_t - \frac{\sigma^2}{2} g^2 v_{gg} - gq_2{\left(\frac{\frac{q_1}{q_2}-v_s}{2}\right)}^2 = 0 $$

With boundary conditions

  • $$ v(t,s,g) = -Cs $$ on $${t=0}$$ or $${s=0}$$ or $${g=0}$$.
  • $$v_g(t,s,\infty) = 0 $$
  • $$v_s(t,\infty,g) = -C $$
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