Parabolic equations with multiple singularities
Partial regularity for flows of -surfaces.
Partial regularity for flows of -surfaces. II.
Partial Regulartiy for Evolution Problems with Discontinuity.
PDE models for chemotactic movements: Parabolic, hyperbolic and kinetic
Modeling the movement of cells (bacteria, amoeba) is a long standing subject and partial differential equations have been used several times. The most classical and successful system was proposed by Patlak and Keller & Segel and is formed of parabolic or elliptic equations coupled through a drift term. This model exhibits a very deep mathematical structure because smooth solutions exist for small initial norm (in the appropriate space) and blow-up for large norms. This reflects experiments on...
Periodic solutions for an evaporation problem with a Signorini type boundary condition
Periodic solutions for Sellers type diffusive energy balance model in climatology
Periodic solutions of degenerate differential equations in vector-valued function spaces
Let A and M be closed linear operators defined on a complex Banach space X. Using operator-valued Fourier multiplier theorems, we obtain necessary and sufficient conditions for the existence and uniqueness of periodic solutions to the equation d/dt(Mu(t)) = Au(t) + f(t), in terms of either boundedness or R-boundedness of the modified resolvent operator determined by the equation. Our results are obtained in the scales of periodic Besov and periodic Lebesgue vector-valued spaces.
Periodic solutions of evolution -Laplacian equations with a nonlinear convection term.
Perturbations singulières de problèmes aux limites, non linéaires, «paraboliques dégénérés-hyperboliques»
Problema di Stefan in spazi di Nikol'skij con peso
Propagation of perturbations in thin capillary film equations with nonlinear diffusion and convection.
Properties of the fast diffusion equation and its multidimensional exact solutions.
Pullback attractors for non-autonomous parabolic equations involving grushin operators.
Pullback attractors for nonautonomous parabolic equations involving weighted p-Laplacian operators
Using the asymptotic a priori estimate method, we prove the existence of pullback attractors for nonautonomous quasilinear degenerate parabolic equations involving weighted p-Laplacian operators in bounded domains, without restriction on the growth order of the polynomial type nonlinearity and on the exponential growth of the external force. The results obtained improve some recent ones for nonautonomous reaction-diffusion equations. Moreover, a relationship between pullback attractors and uniform...