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The Benney equation in 1+1 dimensions is the nonlinear partial differential equation ...

Gives a lower bound for the inner product (Lu,u), where L is a linear elliptic real differential operator of order m, and u has compact support.

The partial differential equation u_t=del ·[M(u)del ((partialf)/(partialu)-Kdel ^2u)].

The partial differential equation u_(xxx)-1/8u_x^3+u_x(Ae^u+Be^(-u))=0.

The system of partial differential equations u_t+u_x = v^2-u^2 (1) v_t-v_x = u^2-v^2. (2)

Partial differential equation boundary conditions which give the value of the function on a surface, e.g., T=f(r,t).

The system of partial differential equations u_t = (u^2-u_x+2v)_x (1) v_y = (2uv+v_x)_x. (2)

The system of partial differential equations u_t = u_(xx)+u(u-a)(1-u)+w (1) w_t = epsilonu. (2)

The system of partial differential equations f_x = 2fgc(x-t) (1) g_t = 2fgc(x-t). (2)

The partial differential equation u_t+2uu_x-nuu_(xx)+muu_(xxx)=0.