On an initial-boundary value problem for a class of nonlinear Schroedinger equations
- Sichuan Normal Univ., Chengdu (China)
Let {Omega} be a bounded domain in R{sup n} with smooth boundary {partial_derivative}{Omega}. Consider the initial-boundary value problem iu{sub t} - {Delta}u = f(u), t > O, x {epsilon} {Omega}, u(O,x) = u{sub O}(x), x {epsilon} {Omega}, u(t,x) = O, t {ge} O, x {epsilon} {partial_derivative} {Omega}, where i{sup 2} = -1, {Delta} is the Laplace operator, f(u) is the nonlinear term, and u{sub O} is a given complex-valued function. The Cauchy problem for the equation in R{sup n} has been studied by S. Klainerman etc. The initial-boundary value problem for has also been studied authors, but the nonlinear terms considered by these authors are classical ones such as f(u) = cu/u/{sup p}(p > O, c {epsilon} R). Here we consider non-classical nonlinear terms such as f(u) = a{vert_bar}u{vert_bar}{sup p+1} + ib{vert_bar}u{sup p+1} (p > O; a,b {epsilon} R). In the domain {Omega}, we introduce the linear eigenvalue problem of the Laplace operator: {Delta} {phi} + {phi} = O, x {epsilon} {Omega}, {phi}(x) = O, x {epsilon}{partial_derivative}{Omega}. 6 refs.
- Sponsoring Organization:
- USDOE
- OSTI ID:
- 437115
- Journal Information:
- Communications in Partial Differential Equations, Vol. 21, Issue 5-6; Other Information: PBD: 1996
- Country of Publication:
- United States
- Language:
- English
Similar Records
A fast solver for systems of reaction-diffusion equations.
Infinitely many solutions of a quasilinear elliptic problem with an oscillatory potential