Related papers: Principal eigenvalue and maximum principle for coo…
The paper is concerned with a system consisting of two coupled nonlinear parabolic equations with a cross-diffusion term, where the solutions at positive times define the initial states. The equations arise as steady state equations of an…
We study a nonlinear coupled system of partial differential equations arising from thermo--reaction--phase models. The system combines a heat diffusion equation, temperature-dependent chemical reactions of Arrhenius type, and a phase…
We consider a new algorithm in light of the min-max Collatz-Wielandt formalism to compute the principal eigenvalue and the eigenvector (eigen-function) for a class of positive Perron-Frobenius-like operators. Such operators are natural…
We provide a proof of strong maximum and minimum principles for fully nonlinear uniformly parabolic equations of second order. The approach is of parabolic nature, slightly differs from the earlier one proposed by L. Nirenberg and does not…
We investigate global and local regularity of generalized solutions to parabolic initial-boundary value problem for Petrovskii system of second order differential equations. Results are formulated in terms of the belonging of right-hand…
In this paper, we consider the stochastic optimal control problem for the interacting particle system. We obtain the stochastic maximum principle of the optimal control system by introducing a generalized backward stochastic differential…
The paper studies the solvability for square systems of pseudodifferential operators. We assume that the system is of principal type, i.e., the principal symbol vanishes of first order on the kernel. We shall also assume that the…
We introduce a unified framework for the construction of convolutions and product formulas associated with a general class of regular and singular Sturm-Liouville boundary value problems. Our approach is based on the application of the…
We consider the most general class of linear boundary-value problems for higher-order ordinary differential systems whose solutions and right-hand sides belong to the corresponding Sobolev spaces. For parameter-dependent problems from this…
We establish certain maximum principles for a class of strongly coupled elliptic (or cross diffusion) systems of $m\ge2$ equations. The reaction parts can be non cooperative. These new results will be crucial in obtaining coexistence and…
The strong maximum principle ((SMP) in short) for subsolutions of the radiative transfer type equations is shown in this paper. We treat a general class of integro-differential equations, defined in the product space of the space variable…
Proposed is a new formal approach for solution of extreme multi-criteria problems transforming them into single-criterion mathematical models, without any additional information. Transforming rules are based on comparison standards and…
In this paper, we study the higher regularity theory of a mixed-type parabolic problem. We extend the recent work of \cite{DMR} to construct solutions that have an arbitrary number of derivatives in Sobolev spaces. To achieve this, we…
In this communication, we prove some important limits of the principal eigenvalue for nonlocal operator of Neumann type with respect to the parameters, which are significant in the understanding of dynamics of biological populations. We…
A classical problem in Complex Dynamics on hyperbolic domains is to characterize the hyperbolic step of parabolic functions. This topic has been studied by several authors, leading to different results and providing characterizations that…
The discrete Laplace operator on a triangulated polyhedral surface is related to geometric properties of the surface. This paper studies extremum problems for eigenvalues of the discrete Laplace operators. Among all triangles, an…
To what extent is the maximum modulus principle for scalar-valued analytic functions valid for matrix-valued analytic functions? In response, we discuss some maximum norm principles for such functions that do not appear to be widely known,…
We consider an elliptic operator in which the second-order term is very small in one direction. In this regime, we study the behaviour of the principal eigenfunction and of the principal eigenvalue. Our first result deals with the limit of…
Pseudo-differential operator equations with parameter are studied. Uniform separability properties and resolvent estimates are obtained in terms of fractional derivatives. Moreover, maximal regularity properties of the pseudo-differential…
The paper focuses on positive solutions to a coupled system of parabolic equations with nonlocal initial conditions. Such equations arise as steady-state equations in an age-structured predator-prey model with diffusion. By using global…