Theoretical or Computational problem. A possible blow-up of the adjoint system

[DRuizB]

-I started a simulation with my code for a semilinear heat equation. -I set a non-linearity that might have a blow-up for certain initial conditions. -For such non-linarity there are theoretical results that say: even if there might be a blow up for a certain initial data, we can build a control that avoids the blow up. -I set an initial data for which there is no blow-up before the integration time T=1 (it may exist afterwards). -One can see that the free dynamics grows but it does not blow up. -HOWEVER, THE CONTROLLED DYNAMICS BLOWS-UP when the target of the optimal control was 0.

• MOREOVER THE COMPUTED CONTROL IS EQUAL TO ZERO.

Here there is the code that I used and the graphics plotted. (note that the controlled dynamics is not integrated over all [0,1])

The function to be executed is plots.m but it requires the other one as well as the whole DyCon toolbox

SLSD1doptimalnullcontrol.txt

plots.txt

[DRuizB]

Another issue, our program does not interpret well symbolically piecewise functions. It basically crashes.

Try the same code above changing the non-linearity by:

aa=5; cc=0.20; syms G(x); G(x) = piecewise(x<=-aa, -2aa^2xcc-2aaaaaacc, aa<=x, -2aaaaxcc+2aaaaaacc, -aa<x<aa, -ccx(x-aa)(x+aa));

Matlab console output: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Error using symengine Unable to generate code for piecewise for use in anonymous functions.

Error in sym/matlabFunction>mup2mat (line 404) res = mupadmex('symobj::generateMATLAB',r.s,ano,spa,0);

Error in sym/matlabFunction>mup2matcell (line 374) r = mup2mat(c{1},true,sparseMat);

Error in sym/matlabFunction (line 188) body = mup2matcell(funs, opts.Sparse);

Error in ode (line 94) obj.numF = matlabFunction(obj.symF);

Error in SLSD1doptimalnullcontrol (line 68) odeEqn2 = ode(Fsym,symY,symU,'Y0',Y0,'T',T);

Error in plots (line 30) [a,b,c,d]=SLSD1doptimalnullcontrol(N,1,G,T,beta,[0.25,0.75],y0); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%