42 citations · 126 across the 30 of their papers we have counts for
10 papers · 2 filters
Persistence of pulses for certain reaction-diffusion equations in dimensions two and three
Vitali Vougalter
We address the persistence under a perturbation of stationary pulse solutions of some reaction-diffusion type equations in dimensions d=2,3 and evaluate the asymptotic approximatio…
Existence of stationary solutions for some integro-differential equations with the double scale anomalous diffusion
Vitali Vougalter, Vitaly Volpert
The paper is devoted to the investigation of the solvability of an integro-differential equation in the case of the double scale anomalous diffusion with a sum of two negative Lapl…
Existence of solutions for some systems of superdiffusive integro-differential equations in population dynamics depending on the natality and mortality rates
Vitali Vougalter
We prove the existence of stationary solutions for some systems of reaction-diffusion type equations with superdiffusion in the corresponding H^2 spaces. Our method is based on the…
Stability and instability of constant stationary solutions to some integro-differential equations
Yuming Chen, Vitali Vougalter
We consider some reaction-diffusion equations describing systems with the nonlocal consumption of resources and the intraspecific competition. Sharp conditions on the coefficients…
Solvability of some integro-differential equations with the logarithmic Laplacian
Vitali Vougalter, Vitaly Volpert
We address the existence in the sense of sequences of solutions for a certain integro-differential type problem involving the logarithmic Laplacian. The argument is based on the fi…
On the existence of solutions for a class of systems of integro-differential equations with the logarithmic Laplacian and drift
Yuming Chen, Vitali Vougalter
In this article, we consider a system of integro-differential equations in L^2(R, R^N), which contains the logarithmic Laplacian in the presence of transport terms. The linear oper…
Existence of solutions for a class of integro-differential equations with the logarithmic Laplacian and transport
Yuming Chen, Vitali Vougalter
In this paper, we consider an integro-differential equation in L^2(R), which involves the logarithmic Laplacian in the presence of a drift term. The linear operator associated with…
On the well-posedness of some model arising in the mathematical biology
Messoud Efendiev, Vitali Vougalter
In the article we establish the global well-posedness in W^{1, 2, 2}(R\times R^{+}) of the integro-differential equation in the case of the anomalous diffusion when the one dimensi…
Solvability of a class of systems of quadratic integral equations
Yuming Chen, Vitali Vougalter
The article is devoted to the existence of solutions of a certain system of quadratic integral equations in H^1(R, R^N). We show the existence of a perturbed solution by using a fi…
On the solvability of some systems of integro-differential equations with and without a drift
Messoud Efendiev, Vitali Vougalter
We prove the existence of solutions for some integro-differential systems containing equations with and without the drift terms in the H^2 spaces by virtue of the fixed point techn…