Nonlinear Galerkin Methods: The Finite Elements Case.
Nonlinear Heat Equation with a Fractional Laplacian in a Disk
For the nonlinear heat equation with a fractional Laplacian , 1 < α ≤ 2, the first initial-boundary value problem in a disk is considered. Small initial conditions, homogeneous boundary conditions, and periodicity conditions in the angular coordinate are imposed. Existence and uniqueness of a global-in-time solution is proved, and the solution is constructed in the form of a series of eigenfunctions of the Laplace operator in the disk. First-order long-time asymptotics of the solution is obtained....
Nonlinear integroparabolic equations on unbounded domains: existence of classical solutions with special properties.
Nonlinear monotone semigroups and viscosity solutions
Nonlinear multidimensional parabolic-hyperbolic equations.
Nonlinear nonlocal evolution problems.
We consider a class of nonlinear parabolic problems where the coefficients are depending on a weighted integral of the solution. We address the issues of existence, uniqueness, stationary solutions and in some cases asymptotic behaviour.
Nonlinear parabolic boundary value problems in the Orlicz-Sobolev spaces
Nonlinear parabolic equations with natural growth in general domains
We prove an existence result for a class of parabolic problems whose principal part is the -Laplace operator or a more general Leray-Lions type operator, and featuring an additional first order term which grows like . Here the spatial domain can have infinite measure, and the data may be not regular enough to ensure the boundedness of solutions. As a consequence, solutions are obtained in a class of functions with exponential integrability. An existence result of bounded solutions is also given...
Nonlinear parabolic equations with natural growth terms and measure initial data
Nonlinear parabolic equations with the mixed nonlinear and nonstationary boundary conditions
Nonlinear parabolic problems on manifolds, and a nonexistence result for the noncompact Yamabe problem.
Nonlinear parabolic problems with Neumann-type boundary conditions and -data.
Nonlinear parabolic variational inequalities
Nonlinear perturbation of balayage spaces.
Nonlinear perturbations of linear elliptic and parabolic problems at resonance : existence of multiple solutions
Nonlinear reaction-diffusion models of self-organization and deterministic chaos: theory and possible applications to description of electrical cardiac activity and cardiovascular circulation.
Nonlinear singular integral inequalities for functions in two and independent variables.
Non-linear stability analysis of higher order dissipative partial differential equations.
Non-linear stationary parabolic boundary value problems in an infinite cylinder
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...