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We consider a model for the evolution of damage in elastic materials originally proposed by Michel Fremond. For the corresponding PDE system we prove existence and uniqueness of a local in time strong solution. The main novelty of our result stands in the fact that, differently from previous contributions, we assume no occurrence of any type of regularizing terms.
In this paper we consider the hyperbolic-elliptic Ishimori initial-value problem. We prove that such system is locally well-posed for small data in $H^{s}$ level space, for $s> 3/2$. The new ingredient is that we develop the methods of Ionescu and Ke
Proving local well-posedness for quasilinear problems in pdes presents a number of difficulties, some of which are universal and others of which are more problem specific. While a common standard, going back to Hadamard, has existed for a long time,
We consider a dilute suspension of dumbbells joined by a finitely extendible nonlinear elastic (FENE) connector evolving under the classical Warner potential $U(s)=-frac{b}{2} log(1-frac{2s}{b})$, $sin[0,frac{b}{2})$. The solvent under consideration
In this paper, we are concerned with the motion of electrically conducting fluid governed by the two-dimensional non-isentropic viscous compressible MHD system on the half plane, with no-slip condition for velocity field, perfect conducting condition
We consider a state-of-the-art ferroelectric phase-field model arising from the engineering area in recent years, which is mathematically formulated as a coupled elliptic-parabolic differential system. We utilize a fixed point theorem based on the ma