Stabilization of the critical nonlinear Klein-Gordon equation with variable coefficients on R3
Texas State University, Department of Mathematics
We prove the exponential stability of the defocusing critical semilinear wave equation with variable coefficients and locally distributed damping on R3. The construction of the variable coefficients is almost equivalent to the geometric control condition. We develop the traditional Morawetz estimates and the compactness-uniqueness arguments for the semilinear wave equation to prove the unique continuation result. The observability inequality and the exponential stability are obtained subsequently.
Critical semilinear wave equation, Variable coefficients, Stability, Morawetz estimates, Riemannian geometry, Unique continuation
Fu, S. R., & Ning, Z. H. (2022). Stabilization of the critical nonlinear Klein-Gordon equation with variable coefficients on R3. <i>Electronic Journal of Differential Equations, 2022</i>(59), pp. 1-18.
Attribution 4.0 International