Grozdena Todorova

Strong instability of standing waves for the nonlinear klein-gordon equation and the klein-gordon-zakharov system

The orbital instability of ground state standing waves

Decay estimates for wave equations with variable coefficients

e^{i\omega t}\phi_{\omega}(x)

THE GENERALIZED DIFFUSION PHENOMENON AND APPLICATIONS

for the nonlinear Klein–Gordon equation has been known in the domain of all frequencies ω for the supercritical case and for frequencies strictly less than a critical frequency

Critical Exponent for a Nonlinear Wave Equation with Damping

\omega_c

Existence for a nonlinear wave equation with damping and source terms

in the subcritical case. We prove the strong instability of ground state standing waves for the entire domain above. For the case when the frequency is equal to the critical frequency

Blow-up for nonlinear dissipative wave equations in Rn

\omega_c

Weighted L2-estimates for dissipative wave equations with variable coefficients

we prove strong instability for all radially symmetric standing waves

Wave equations with strong damping in Hilbert spaces

e^{i\omega_c t}\varphi(x)

Remarks on global existence and blowup for damped nonlinear Schrödinger equations

. We prove similar strong instability results for the Klein–Gordon–Zakharov system.

Critical Exponent for Semilinear Wave Equations with Space-Dependent Potential

We establish weighted L 2 -estimates for dissipative wave equations with variable coefficients that exhibit a dissipative term with a space dependent potential. These results yield decay estimates for the energy and the L 2 —norm of solutions. The proof is based on the multiplier method where multipliers are specially engineered from asymptotic profiles of related parabolic equations.