Related papers: On a non-local problem for parabolic-hyperbolic eq…
In this small paper, we study a boundary value problem for an equation of parabolic-hyperbolic type. The goal is to show how we can prove existence and uniqueness theorem for a regular solution.
We study local and global existence of solutions for some semilinear parabolic initial boundary value problems with autonomous nonlinearities having a "Newtonian" nonlocal term.
In this paper, a nonlinear inverse boundary value problem for the second-order hyperbolic equation with nonlocal conditions is studied. To investigate the solvability of the original problem, we first consider an auxiliary inverse boundary…
In this paper we consider an initial boundary value problem for a semilinear parabolic equation with nonlinear nonlocal boundary condition. We prove comparison principle, the existence theorem of a local solution and study the problem of…
In this paper we study one dimensional parabolic free boundary value problem with a nonlocal (integro-differential) condition on the free boundary. We establish global existence-uniqueness of classical solutions assuming that the…
A problem with non-classical conditions on all the boundary not requiring agreement conditions is considered for a sixth order pseudoparapolic equation. The equivalence of these conditions with the classic boundary condition is…
In the paper, the contact - boundary value problem with non-classical conditions not requiring agreement conditions is considered for a pseudoparabolic equation. The equivalence of these conditions is substantiated in the case if the…
By topological arguments, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions of a class of perturbed nonlinear integral equations. These type of integral equations arise, for example,…
We prove global existence and blow-up of solutions of initial-boundary value problem for nonlinear nonlocal parabolic equation with nonlinear nonlocal boundary condition. Obtained results depend on the behavior of variable coefficients for…
The goal of this note is to study nonlinear parabolic problems nonlocal in time and space. We first establish the existence of a solution and its uniqueness in certain cases. Finally we consider its asymptotic behaviour.
The aim of this work is studding the behavior of solutions of initial boundary problem for degenerated nonlinear parabolic equation of the second order, conditions of existence and non-existence in whole by time solutions, is establish.
We consider a quasi-linear parabolic equation with nonlinear dynamic boundary conditions occurring as a natural generalization of the semilinear reaction-diffusion equation with dynamic boundary conditions. The corresponding class of…
Some systems of parabolic equations with nonlocal initial conditions are studied. The systems arise when considering steady-state solutions to diffusive age-structured cooperative or competing species. Local and global bifurcation…
In this paper we consider initial boundary value problem for nonlinear nonlocal parabolic equation with absorption under nonlinear nonlocal boundary condition and nonnegative initial datum. We prove comparison principle, global existence…
We study well-posedness of degenerate mixed-type parabolic-hyperbolic equations $$ \partial_tu+\text{div}\big(f(u)\big)=\mathcal{L}[b(u)] $$ on bounded domains with general Dirichlet boundary/exterior conditions. The nonlocal diffusion…
The paper deals with second order parabolic equations on bounded domains with Dirichlet conditions in arbitrary Euclidean spaces. Their interest comes from being models for describing reaction-diffusion processes in several frameworks. A…
Motivated by a mathematical model for the transport of morphogenes in biological systems, we study existence and uniqueness of entropy solutions for a mixed initial-boundary value problem associated with a nonlinear flux--limited diffusion…
In this paper, a new type of comparison theorem is presented for some initial-boundary value problems of second order nonlinear parabolic systems with nonlinear boundary conditions. This comparison theorem has an advantage over the…
In the present work we investigate the Tricomi problem with integral gluing condition for parabolic-hyperbolic equation with the Caputo fractional order derivative. Using the method of energy integrals we prove the uniqueness of the…
In this Note, we review the main existing results, methods, and some key open problems on the controllability of nonlinear hyperbolic and parabolic equations. Especially, we describe our recent universal approach to solve the local…