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Strong solutions for strongly damped quasilinear wave equations. (English) Zbl 0638.35054
The legacy of Sonya Kovalevskaya, Proc. Symp., Radcliffe Coll. 1985, Contemp. Math. 64, 219-237 (1987).
[For the entire collection see Zbl 0601.00007.]
From the author’s summary: Quasilinear strongly damped wave equations \[ u_{tt}=\Delta u_ t+div(g(\nabla u))+f \] are studied in bounded space-time cylinders \(\Omega \times [0,T]\subset {\mathbb{R}}^{n+1}\) together with initial conditions and Dirichlet or Neumann type boundary conditions. For isotropic nonlinearities g with natural ellipticity properties and controlled growth and for arbitrary initial data, global solutions are constructed that satisfy the equation almost everywhere. In the case of radially symmetric data, global classical solutions are found.
Reviewer: H.Lange

MSC:
35L70 Second-order nonlinear hyperbolic equations
35A30 Geometric theory, characteristics, transformations in context of PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B65 Smoothness and regularity of solutions to PDEs