Infinitely Many Traveling Wave Solutions of a Gradient System
Copyright policy )Infinitely Many Traveling Wave Solutions of a Gradient System
We consider a system of equations of the form u t = u x x + ∇ F ( u ) {u_t} = {u_{xx}} + \nabla F(u) . A traveling wave solution of this system is one of the form u ( x , t ) = U ( z ) , z = x + θ t u(x,\,t) = U(z),\,z = x + \theta t . Sufficient conditions on F ( u ) F(u) are given to guarantee the existence of infinitely many traveling wave solutions.
traveling wave solution, reaction-diffusion equations, Reaction-diffusion equations, Asymptotic behavior of solutions to PDEs, existence, Nonlinear parabolic equations, General existence and uniqueness theorems (PDE), infinitely many traveling wave solutions, Second-order parabolic systems
traveling wave solution, reaction-diffusion equations, Reaction-diffusion equations, Asymptotic behavior of solutions to PDEs, existence, Nonlinear parabolic equations, General existence and uniqueness theorems (PDE), infinitely many traveling wave solutions, Second-order parabolic systems
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