Related papers: A nonlinear inequality and applications
THis work is a survey of a few nonlinear PDE based models in image restoring.
Real-life problems are governed by equations which are nonlinear in nature. Nonlinear equations occur in modeling problems, such as minimizing costs in industries and minimizing risks in businesses. A technique which does not involve the…
The generalization of the simplest equation method to look for exact solutions of systems of nonlinear differential equations is presented. The exact solutions of NDE systems describing the evolution of two interacting populations in two…
Some uniform decay estimates are established for solutions of the following type of retarded integral inequalities: $$y(t)\leq E(t,\tau)||y_\tau||+\int_\tau^t K_1(t,s)||y_s||ds+\int_t^\infty K_2(t,s)||y_s||ds+\rho, \hspace{0.5cm}…
The properties of nonlinear PDEs that generate filtered solutions are explored with particular attention given to the constraints on the residual term. The analysis is carried out for nonlinear PDEs with an emphasis on evolution problems…
Modelling real world systems frequently requires the solution of systems of nonlinear equations. A number of approaches have been suggested and developed for this computational problem. However, it is also possible to attempt solutions…
Using the rudiments of pde jets theory in a nonstandard setting, we first deepen and extend previous nonstandard existence results for generalized solutions of linear differential equations and second extend the previous results for linear…
The nonlinear hyperbolic system of pde's governing the evolution of the deformation of isotropic hyperelastic materials is considered. In the absence of boundaries and with an additional nonresonance or null condition, the system has global…
A version of the nonlinear Hodge equations is introduced in which the irrotationality condition is weakened. An elliptic estimate for solutions is derived.
A new delay equation is introduced to describe the punctuated evolution of complex nonlinear systems. A detailed analytical and numerical investigation provides the classification of all possible types of solutions for the dynamics of a…
A new method is given for proving the global existence of the solution to nonlinear Volterra integral equations. A bound on the solution is derived. The results are based on a nonlinear inequality proved by the author earlier.
In this paper, we study the global existence and regularity of H\"older continuous solutions for a series of nonlinear partial differential equations describing nonlinear waves.
Under a precise nonlinearity-diffusivity condition we establish the decay of space-periodic entropy solutions of a multidimensional degenerate nonlinear parabolic equation.
Qualitative properties of non-negative solutions to a quasilinear degenerate parabolic equation with an absorption term depending solely on the gradient are shown, providing information on the competition between the nonlinear diffusion and…
Travelling and rotating waves are ubiquitous phenomena observed in time dependent PDEs modelling the combined effect of dissipation and non-linear interaction. From an abstract viewpoint they appear as relative equilibria of an equivariant…
New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption…
We study a nonlinear pseudodifferential equation describing the dynamics of dislocations. The long time asymptotics of solutions is described by the self-similar profiles.
In this paper we consider second order evolution equations with bounded damping. We give a characterization of a non uniform decay for the damped problem using a kind of observability estimate for the associated undamped problem.
We study the existence and uniqueness of solutions of a nonlinear integro-differential problem which we reformulate introducing the notion of the decreasing rearrangement of the solution. A dimensional reduction of the problem is obtained…
A general formalism to solve nonlinear differential equations is given. Solutions are found and reduced to those of second order nonlinear differential equations in one variable. The approach is uniformized in the geometry and solves…