Fractional flux and non-normal diffusion.
Fundamental solutions to the fractional heat conduction equation in a ball under Robin boundary condition
The central symmetric time-fractional heat conduction equation with Caputo derivative of order 0 < α ≤ 2 is considered in a ball under two types of Robin boundary condition: the mathematical one with the prescribed linear combination of values of temperature and values of its normal derivative at the boundary, and the physical condition with the prescribed linear combination of values of temperature and values of the heat flux at the boundary, which is a consequence of Newton’s law of convective...
Global and non-global existence of solutions to a nonlocal and degenerate quasilinear parabolic system
The paper deals with positive solutions of a nonlocal and degenerate quasilinear parabolic system not in divergence form with null Dirichlet boundary conditions. By using the standard approximation method, we first give a series of fine a priori estimates for the solution of the corresponding approximate problem. Then using the diagonal method, we get the local existence and the bounds of the solution to this problem. Moreover, a necessary and sufficient condition for the non-global existence...
Global classical solutions to the Cauchy problem for a nonlinear wave equation.
Global existence and blow-up solutions and blow-up estimates for some evolution systems with -Laplacian with nonlocal sources.
Global existence and polynomial decay for a problem with Balakrishnan-Taylor damping
A viscoelastic Kirchhoff equation with Balakrishnan-Taylor damping is considered. Using integral inequalities and multiplier techniques we establish polynomial decay estimates for the energy of the problem. The results obtained in this paper extend previous results by Tatar and Zaraï [25].
Global existence for a hyperbolic integrodifferential inverse problem.
Global existence for a semilinear prabolic Volterra equation.
Global existence for functional semilinear integro-differential equations
In this paper, we study the global existence of solutions for first and second order initial value problems for functional semilinear integrodifferential equations in Banach space, by using the Leray-Schauder Alternative or the Nonlinear Alternative for contractive maps.
Global existence for the conserved phase field model with memory and quadratic nonlinearity.
Global existence of solutions for the non linear Boltzmann equation of semiconductor physics.
In this paper we give a proof of the existence and uniqueness of smooth solutions for the nonlinear semiconductor Boltzmann equation. The method used allows to obtain global existence in time and uniqueness for dimensions 1 and 2. For dimension 3 we can only assure local existence in time and uniqueness. First, we define a sequence of solutions for a linearized equation and then, we prove the strong convergence of the sequence in a suitable space. The metod relies on the use of interpolation estimates...
Global (in time) solution of the approximate nonlinear string equation of G. F. Carrier and R. Narasimha
Global in time solutions to quasilinear telegraph equations involving operators with time delay
The existence of small global (in time) solutions to an abstract evolution equation containing a damping term is proved. The result is then applied to fully nonlinear telegraph equations and to nonlinear equations involving operators with time delay.
Global strong solutions of Vlasov's equation---necessary and sufficient conditions for their existence
Gradient flows of the entropy for jump processes
We introduce a new transport distance between probability measures on that is built from a Lévy jump kernel. It is defined via a non-local variant of the Benamou–Brenier formula. We study geometric and topological properties of this distance, in particular we prove existence of geodesics. For translation invariant jump kernels we identify the semigroup generated by the associated non-local operator as the gradient flow of the relative entropy w.r.t. the new distance and show that the entropy is...
Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations
This paper is concerned with the Hölder regularity of viscosity solutions of second-order, fully non-linear elliptic integro-differential equations. Our results rely on two key ingredients: first we assume that, at each point of the domain, either the equation is strictly elliptic in the classical fully non-linear sense, or (and this is the most original part of our work) the equation is strictly elliptic in a non-local non-linear sense we make precise. Next we impose some regularity and growth...
Homogenization of a linear transport equation with time depending coefficient
Identification of two degenerate time- and space-dependent kernels in a parabolic equation.
Infinite systems of first order PFDEs with mixed conditions
We consider mixed problems for infinite systems of first order partial functional differential equations. An infinite number of deviating functions is permitted, and the delay of an argument may also depend on the spatial variable. A theorem on the existence of a solution and its continuous dependence upon initial boundary data is proved. The method of successive approximations is used in the existence proof. Infinite differential systems with deviated arguments and differential integral systems...
Inverse problems for memory kernels by Laplace transform methods.