Weak solutions for nonlinear waves in adhesive phenomena
نویسندگان
چکیده
Abstract We discuss a notion of weak solution for semilinear wave equation that models the interaction an elastic body with rigid substrate through adhesive layer, relying on results in [2]. Our analysis embraces vector-valued case arbitrary dimension as well non-local operators (e.g. fractional Laplacian).
منابع مشابه
Convergence Rates to Nonlinear Di®usion Waves for Weak Entropy Solutions to p-System with Damping
In this paper, we study the asymptotic behavior of weak entropy solutions to the Cauchy problem of the so-called p-system with damping. The convergence rates to nonlinear di®usion waves are obtained. The analysis is based on the viscosity method and energy method.
متن کاملExistence and uniqueness of weak solutions for a class of nonlinear divergence type diffusion equations
In this paper, we study the Neumann boundary value problem of a class of nonlinear divergence type diffusion equations. By a priori estimates, difference and variation techniques, we establish the existence and uniqueness of weak solutions of this problem.
متن کاملNonlinear Fresnel diffraction of weak shock waves.
Fresnel diffraction at a straight edge is revisited for nonlinear acoustics. Considering the penumbra region as a diffraction boundary layer governed by the KZ equation and its associated jump relations for shocks, similarity laws are established for the diffraction of a step shock, an "N" wave, or a periodic sawtooth wave. Compared to the linear case described by the well-known Fresnel functio...
متن کاملWeak localization with nonlinear bosonic matter waves
We investigate the coherent propagation of dilute atomic Bose-Einstein condensates through irregularly shaped billiard geometries that are attached to uniform incoming and outgoing waveguides. Using the mean-field description based on the nonlinear Gross-Pitaevskii equation, we develop a diagrammatic theory for the self-consistent stationary scattering state of the interacting condensate, which...
متن کاملSteep. Short-Crested Waves and Related Phenomena
Steep, short-crested waves, as well as a large variety of three-dimensional propagating wave patterns have been created in laboratory, utilizing a plunging half-cone. Monochromatic waves, over a range of frequencies and amplitudes through breaking and including soliton wave groups near resonance, have been observed and studied in a small wave flume. This monochromatic wavemaker creates complex ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annali Dell'universita' Di Ferrara
سال: 2022
ISSN: ['1827-1510', '0430-3202']
DOI: https://doi.org/10.1007/s11565-022-00398-6