Low Regularity Semi-linear Wave Equations
نویسنده
چکیده
We prove local well-posedness results for the semi-linear wave equation for data in H , 0 < < n?3 2(n?1) , extending the previously known results for this problem. The improvement comes from an introduction of a two-scale Lebesgue space X r;p k .
منابع مشابه
Se p 19 97 LOW REGULARITY SEMI - LINEAR WAVE EQUATIONS
We prove local well-posedness results for the semi-linear wave equation for data in H γ , 0 < γ < n−3 2(n−1) , extending the previously known results for this problem. The improvement comes from an introduction of a two-scale Lebesgue space X r,p k .
متن کاملSemilinear Wave Equations
We survey existence and regularity results for semi-linear wave equations. In particular, we review the recent regularity results for the u5-Klein Gordon equation by Grillakis and this author and give a self-contained, slightly simplified proof.
متن کاملGlobal Low Regularity Solutions of Quasi-linear Wave Equations
In this paper we prove the global existence and uniqueness of the low regularity solutions to the Cauchy problem of quasi-linear wave equations with radial symmetric initial data in three space dimensions. The results are based on the end-point Strichartz estimate together with the characteristic method.
متن کاملInvestigation of the Effects of Non-Linear and Non-Homogeneous Non-Fourier Heat Conduction Equations on Temperature Distribution in a Semi-Infinite Body
In this paper, the non-Fourier heat conduction in a semi-infinite body was examined. The heat wave non-Fourier heat conduction model was used for thermal analysis. Thermal conductivity was assumed temperature-dependent which resulted in a non-linear equation. The heat source was also considered temperature-dependent which resulted in a non-homogeneous equation. The Mac-Cormack predictor-correct...
متن کاملFinite-dimensional Attractors for the Quasi-linear Strongly-damped Wave Equation
We present a new method of investigating the so-called quasi-linear strongly damped wave equations ∂ t u− γ∂t∆xu−∆xu+ f(u) = ∇x · φ ′(∇xu) + g in bounded 3D domains. This method allows us to establish the existence and uniqueness of energy solutions in the case where the growth exponent of the non-linearity φ is less than 6 and f may have arbitrary polynomial growth rate. Moreover, the existenc...
متن کامل