Global Regular Solutions for the Nonhomogeneous Carrier Equation

N. A. LARKIN

《Mathematical Problems in Engineering》 2002卷 (2002/12) Pp. 15-31

https://doi.org/10.1080/10241230211382

摘要

We study in a n + 1-dimensional cylinder Q global solvability of the mixed problem for the nonhomogeneous Carrier equation u_(tt)-M(x, t, ||u(t)||^2) ∆u+g(x, t, u_t)=f(x, t) without restrictions on a size of initial data and f(x, t). For any natural n, we prove existence, uniqueness and the exponential decay of the energy for global generalized solutions. When n= 2, we prove C^∞(Q)-regularity of solutions.

關鍵字

Carrier equation ； Global smooth solutions ； Existence