Nonlinear systems of parabolic PDE's for phase change problem
Nonlinear Tensor Diffusion in Image Processing
This paper presents and summarize our results concerning the nonlinear tensor diffusion which enhances image structure coherence. The core of the paper comes from [3, 2, 4, 5]. First we briefly describe the diffusion model and provide its basic properties. Further we build a semi-implicit finite volume scheme for the above mentioned model with the help of a co-volume mesh. This strategy is well-known as diamond-cell method owing to the choice of co-volume as a diamondshaped polygon, see [1]. We...
Nonlinear Time-Fractional Differential Equations in Combustion Science
MSC 2010: 34A08 (main), 34G20, 80A25The application of Fractional Calculus in combustion science to model the evolution in time of the radius of an isolated premixed flame ball is highlighted. Literature equations for premixed flame ball radius are rederived by a new method that strongly simplifies previous ones. These equations are nonlinear time-fractional differential equations of order 1/2 with a Gaussian underlying diffusion process. Extending the analysis to self-similar anomalous diffusion...
Nonlinear transmission problem with a dissipative boundary condition of memory type.
Nonlinear unilateral problems in Orlicz spaces
We prove the existence of solutions of the unilateral problem for equations of the type Au - divϕ(u) = μ in Orlicz spaces, where A is a Leray-Lions operator defined on , and .
Nonlinear variational inequalities of semilinear parabolic type.
Nonlinear vibrations of completely resonant wave equations
We present recent existence results of small amplitude periodic and quasi-periodic solutions of completely resonant nonlinear wave equations. Both infinite-dimensional bifurcation phenomena and small divisors difficulties occur. The proofs rely on bifurcation theory, Nash-Moser implicit function theorems, dynamical systems techniques and variational methods.
Nonlinear Wave Equation with Vanishing Potential
We study the Cauchy problem for utt − ∆u + V (x)u^5 = 0 in 3–dimensional case. The function V (x) is positive and regular, in particular we are interested in the case V (x) = 0 in some points. We look for the global classical solution of this equation under a suitable hypothesis on the initial energy.
Non-Lipschitz coefficients for strictly hyperbolic equations
In the present paper we explain the classification of oscillations and its relation to the loss of derivatives for a homogeneous hyperbolic operator of second order. In this way we answer the open question if the assumptions to get well posedness for weakly hyperbolic Cauchy problems or for strictly hyperbolic Cauchy problems with non-Lipschitz coefficients are optimal.
Nonlocal and initial problems for quasilinear nonstrictly hyperbolic equations with general solutions represented by superpositions of arbitrary functions.
Nonlocal boundary value problem for second order abstract elliptic differential equation.
Nonlocal boundary value problems for elliptic-parabolic differential and difference equations.
Nonlocal conditions for lower semicontinuous parabolic inclusions.
Nonlocal elliptic problems
Some conditions for the existence and uniqueness of solutions of the nonlocal elliptic problem , are given.
Non-local Gel'fand problem in higher dimensions
The non-local Gel’fand problem, with Dirichlet boundary condition, is studied on an n-dimensional bounded domain Ω. If it is star-shaped, then we have an upper bound of λ for the existence of the solution. We also have infinitely many bendings in λ of the connected component of the solution set in λ,v if Ω is a ball and 3 ≤ n ≤ 9.
Nonlocal Poincaré inequalities on Lie groups with polynomial volume growth and Riemannian manifolds
Let G be a real connected Lie group with polynomial volume growth endowed with its Haar measuredx. Given a C² positive bounded integrable function M on G, we give a sufficient condition for an L² Poincaré inequality with respect to the measure M(x)dx to hold on G. We then establish a nonlocal Poincaré inequality on G with respect to M(x)dx. We also give analogous Poincaré inequalities on Riemannian manifolds and deal with the case of Hardy inequalities.
Nonlocal problem for the hyperbolic system of differential equation of the first order.
Nonlocal problems for first order functional partial differential equations
Local existence of generalized solutions to nonlocal problems for nonlinear functional partial differential equations of first order is investigated. The proof is based on the bicharacteristics and successive approximations methods.
Non-local problems for parabolic-hyperbolic equations with deviation from the characteristics and three type-changing lines.
Nonlocal problems for quasilinear functional partial differential equations of first order.
Existence and uniqueness of almost everywhere solutions of nonlocal problems to functional partial differential systems in diagonal form are investigated. The proof is based on the characteristics and fixed point methods.