Weak solutions to a nonlinear variational wave equation with general data

A commonly observed feature of nonnegative solutions to diffusion equations in the whole space R N is their decay to zero as time increases to infinity.. This convergence to zero

Recall that a solution to a partial differential equation is usually referred to as a singular solution if it satisfies (1.2), the main examples being the so-called

It is shown that plane wave solutions to the cubic nonlinear Schr¨ odinger equa- tion on a torus behave orbitally stable under generic perturbations of the initial data that are

In this paper, we study the traveling wave solutions of Allen–Cahn equation with a fractional Laplacian, where the nonlinear reaction is a bistable potential.. If the front of

Key words: nonlinear parabolic equations, gradient term, global existence, bounded solutions, Poincare inequality, blow-up, critical exponent, exponential

- We study the asymptotic behavior in time of solutions to the Cauchy problem for the derivative nonlinear Schrodinger equation.. where a E

When the parameter λ > 0 is large enough, we find two critical points of the corresponding ε-functional which, at the limit as ε → 0, give rise to two distinct nonnegative

We obtain a new class of the heat wave type solutions the construction of which is reduced to the Cauchy problems for nonlinear second order differential equations with a