ﻻ يوجد ملخص باللغة العربية
We study the inverse problem of recovery a non-linearity $f(x,u)$, which is compactly supported in $x$, in the semilinear wave equation $u_{tt}-Delta u+ f(x,u)=0$. We probe the medium with either complex or real-valued harmonic waves of wavelength $sim h$ and amplitude $sim 1$. They propagate in a regime where the non-linearity affects the subprincipal but not the principal term, except for the zeroth harmonics. We measure the transmitted wave when it exits $text{supp}_x f$. We show that one can recover $f(x,u)$ when it is an odd function of $u$, and we can recover $alpha(x)$ when $f(x,u)=alpha(x)u^{2m}$. This is done in an explicit way as $hto0$.
In this paper, we study the blow-up of solutions for semilinear wave equations with scale-invariant dissipation and mass in the case in which the model is somehow wave-like. A Strauss type critical exponent is determined as the upper bound for the ex
In this note, we prove blow-up results for semilinear wave models with damping and mass in the scale-invariant case and with nonlinear terms of derivative type. We consider the single equation and the weakly coupled system. In the first case we get a
In this paper, we study a class of nonlinear Choquard type equations involving a general nonlinearity. By using the method of penalization argument, we show that there exists a family of solutions having multiple concentration regions which concentra
We consider the periodic solutions of a semilinear variable coefficient wave equation arising from the forced vibrations of a nonhomogeneous string and the propagation of seismic waves in nonisotropic media. The variable coefficient characterizes the
We study the inverse problem of recovery a compactly supported non-linearity in the semilinear wave equation $u_{tt}-Delta u+ alpha(x) |u|^2u=0$, in two and three dimensions. We probe the medium with complex-valued harmonic waves of wavelength $h$ an