8.1.3 1.3

8.1.3.1 [2010] Problem 1

problem number 2010

Added March 23, 2019.

Problem Chapter 1.1.3.1, from Handbook of nonlinear partial differential equations by Andrei D. Polyanin, Valentin F. Zaitsev.

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

\[ w_t = a w_{xx} +b w^k \]

Mathematica ✗

ClearAll["Global`*"]; 
pde =  D[w[x, t], t] == a*D[w[x, t], {x, 2}] + b*w[x, t]^k; 
sol =  AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, t], {x, t}], 60*10]];
 

Failed

Maple ✗

restart; 
pde :=  diff(w(x,t),t)= a*diff(w(x,t),x$2) +b*w(x,t)^k; 
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,t))),output='realtime'));
 

sol=()

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8.1.3.2 [2011] Problem 2

problem number 2011

Added March 23, 2019.

Problem Chapter 1.1.3.2, from Handbook of nonlinear partial differential equations by Andrei D. Polyanin, Valentin F. Zaitsev.

Solve for \(w(x,t)\) \[ w_t = w_{xx} +a w+ b w^m \]

Mathematica ✗

ClearAll["Global`*"]; 
pde =  D[w[x, t], t] == D[w[x, t], {x, 2}] + a*w[x, t] + b*w[x, t]^m; 
sol =  AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, t], {x, t}], 60*10]];
 

Failed

Maple ✗

restart; 
pde :=  diff(w(x,t),t)= diff(w(x,t),x$2) +a*w(x,t)+b*w(x,t)^m; 
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,t))),output='realtime'));
 

sol=()

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8.1.3.3 [2012] Problem 3

problem number 2012

Added March 23, 2019.

Problem Chapter 1.1.3.3, from Handbook of nonlinear partial differential equations by Andrei D. Polyanin, Valentin F. Zaitsev.

Solve for \(w(x,t)\) \[ w_t = w_{xx} +a w+ b w^m + c w^{2 m -1} \]

Mathematica ✗

ClearAll["Global`*"]; 
pde =  D[w[x, t], t] == D[w[x, t], {x, 2}] + a*w[x, t] + b*w[x, t]^m + c*w[x, t]^(2*m - 1); 
sol =  AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, t], {x, t}], 60*10]];
 

Failed

Maple ✗

restart; 
pde :=  diff(w(x,t),t)= diff(w(x,t),x$2) +a*w(x,t)+b*w(x,t)^m+c*w(x,t)^(2*m-1); 
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,t))),output='realtime'));
 

sol=()

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8.1.3.4 [2013] Problem 4

problem number 2013

Added March 23, 2019.

Problem Chapter 1.1.3.4, from Handbook of nonlinear partial differential equations by Andrei D. Polyanin, Valentin F. Zaitsev.

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

\[ w_t = w_{xx} +a w^{m -1} + b m w^m - m b^2 w^{2 m -1} \]

Mathematica ✗

ClearAll["Global`*"]; 
pde =  D[w[x, t], t] == D[w[x, t], {x, 2}] + a*w[x, t]^(m - 1) + b*m*w[x, t]^m - m*b^2*w[x, t]^(2*m - 1); 
sol =  AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, t], {x, t}], 60*10]];
 

Failed

Maple ✗

restart; 
pde :=  diff(w(x,t),t)= diff(w(x,t),x$2) +a*w(x,t)^(m-1)+b*m*w(x,t)^m-m*b^2*w(x,t)^(2*m-1); 
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,t))),output='realtime'));
 

sol=()

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