156 HNPDE, chapter 1.1.4

____________________________________________________________________________________

156.1 Problem 1

problem number 1250

Added March 23, 2019.

Problem Chapter 1.1.4.1, from Handbook of nonlinear partial differential equations by Andrei D. Polyanin, Valentin F. Zaitsev.

Solve for \(w(x,t)\)

\[ w_t = a w_{xx} +s_1 (b x+c t)^k+ s_2 w^m \]

Mathematica ✗

ClearAll[w, x, y, n, a, b, m, c, k, alpha, beta, gamma, A, C0, s]; 
 ClearAll[lambda, B, mu, d, g, B, v, f, h, q, p, delta, t]; 
 ClearAll[g1, g0, h2, h1, h0, f1, f2]; 
 ClearAll[a1, a0, b3, b2, b1, b0, c2, c1, c0, k0, k1, k2, s1, s0, k22, k11, k12, s11, s22, s12, s1, s2]; 
 pde = D[w[x, t], t] == a*D[w[x, t], {x, 2}] + s1*(b*x + c*t)^k + s2*w[x, t]^m; 
 sol = AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, t], {x, t}], 60*10]];
 

\[ \text {Failed} \]

Maple ✗

 
unassign('w,x,y,a,b,n,m,c,k,alpha,beta,g,A,f,C,lambda,B,mu,d,s,t'); 
unassign('v,q,p,l,g1,g2,g0,h0,h1,h2,f2,f3,c0,c1,c2,a1,a0,b0,b1,b2'); 
unassign('k0,k1,k2,s0,s1,k22,k12,k11,s22,s12,s11'); 
pde :=  diff(w(x,t),t)= a*diff(w(x,t),x$2) +s1*(b*x+c*t)^k+s2*w(x,t)^m; 
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,t))),output='realtime'));
 

\[ \text { sol=() } \]

This document was compiled using

Text Font: ec-mlmr12

Math Operator Font: rm-mlmr12

Math Letter Font: mlmmi12