2.15.10 Clarke. \(\left ( \theta _t - \gamma e^\theta \right )_{tt} = \left ( \theta _t - e^\theta \right )_{xx}\)

problem number 119

Added December 27, 2018.

Taken from https://en.wikipedia.org/wiki/List_of_nonlinear_partial_differential_equations

Clarke equation. Solve for \(\theta (x,t)\) \[ \left ( \theta _t - \gamma e^\theta \right )_{tt} = \left ( \theta _t - e^\theta \right )_{xx} \]

Mathematica ✗

ClearAll["Global`*"]; 
pde =  D[D[theta[x, t], t] - gamma*Exp[theta[x, t]], {t, 2}] == D[D[theta[x, t], t] - Exp[theta[x, t]], {x, 2}]; 
sol =  AbsoluteTiming[TimeConstrained[DSolve[pde, theta[x, t], {x, t}], 60*10]];
 

Failed

Maple ✗

restart; 
pde := diff(diff(theta(x,t),t)-g*exp(theta(x,t)),t$2) = diff( diff(theta(x,t),t)-exp(theta(x,t)),x$2); 
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,theta(x,t))),output='realtime'));
 

sol=()

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