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24 papers · 1 filter
Boundedness of the solutions of a kind of nonlinear parabolic systems
Emilia Anna Alfano, Luisa Fattorusso, Lubomira Softova
We deal with nonlinear systems of parabolic type satisfying component-wise structural conditions. The nonlinear terms are Carathéodory maps having controlled growth with respect to…
A Carleman estimate and an energy method for a first-order symmetric hyperbolic system
G. Floridia, H. Takase, M. Yamamoto
For a symmetric hyperbolic system of the first order, we prove a Carleman estimate under some positivity condition concerning the coefficient matrices. Next, applying the Carleman…
Inverse problems for first-order hyperbolic equations with time-dependent coefficients
Giuseppe Floridia, Hiroshi Takase
We prove global Lipschitz stability for inverse source and coefficient problems for first-order linear hyperbolic equations, the coefficients of which depend on both space and time…
Backward problems in time for fractional diffusion-wave equation
Giuseppe Floridia, Masahiro Yamamoto
In this article, for a time-fractional diffusion-wave equation $\pppa u(x,t) = -Au(x,t)$, with fractional order , we consider the backward problem in time: dete…
Observability inequalities for degenerate transport equations
Giuseppe Floridia, Hiroshi Takase
In this paper we prove an observability inequality for a degenerate transport equation. First we introduce a local in time Carleman estimate for the degenerate equation, then we ap…
Precise Morrey regularity of the weak solutions to a kind of quasilinear systems with discontinuous data
Luisa Fattorusso, Lubomira Softova
We consider the Dirichlet problem for a class of quasilinear elliptic systems in domain with irregular boundary. The principal part satisfies componentwise coercivity condition and…