Nonlocal diffusion second order partial differential equations
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DOI: 10.1016/j.jde.2016.10.019
Abstract: Abstract The paper deals with a second order integro-partial differential equation in R n with a nonlocal, degenerate diffusion term. Nonlocal conditions, such as the Cauchy multipoint and the weighted mean value problem, are investigated.… read more here.
Keywords: diffusion; partial differential; second order; differential equations ... See more keywords
Nonlocal Harnack inequalities for nonlocal heat equations
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DOI: 10.1016/j.jde.2019.07.006
Abstract: In this paper, applying the De Giorgi method, we obtain nonlocal Harnack inequalities for weak solutions of nonlocal parabolic equations given by an integro-differential operator $\rL_K$ as follows; \begin{equation*}\begin{cases} \rL_K u+\pa_t u=0 &\text{ in $\Om\times(-T,0]$… read more here.
Keywords: inequalities nonlocal; harnack; equations nonlocal; nonlocal harnack ... See more keywords
Existence of solutions for nonlinear Hadamard differential equations with nonlocal conditions
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DOI: 10.1080/09720502.2020.1800226
Abstract: Abstract This paper investigates the existence of solutions for a boundary value problem of Hadamard fractional differential equations with nonlocal conditions. The existence and uniqueness of solutions is derived from Banach’s contraction principle. Then, by… read more here.
Keywords: solutions nonlinear; differential equations; conditions existence; equations nonlocal ... See more keywords
Classical Solutions of Hyperbolic Equations with Nonlocal Potentials
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DOI: 10.1134/s1064562421030157
Abstract: A three-parameter family of global solutions for a two-dimensional hyperbolic differential-difference equation with a nonlocal potential is constructed. A theorem that the obtained solutions are classical is proved. read more here.
Keywords: nonlocal potentials; solutions hyperbolic; equations nonlocal; hyperbolic equations ... See more keywords
Existence and approximate controllability of fractional evolution equations with nonlocal conditions via resolvent operators
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DOI: 10.1515/fca-2020-0011
Abstract: Abstract In this article, we are concerned with the existence of mild solutions as well as approximate controllability for a class of fractional evolution equations with nonlocal conditions in Banach spaces. Sufficient conditions of existence… read more here.
Keywords: evolution equations; approximate controllability; fractional evolution; controllability ... See more keywords
Approximate controllability of fractional stochastic evolution equations with nonlocal conditions
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DOI: 10.1515/ijnsns-2019-0229
Abstract: Abstract This paper deals with the approximate controllability for a class of fractional stochastic evolution equations with nonlocal initial conditions in a Hilbert space. We delete the compactness condition or Lipschitz condition for nonlocal term… read more here.
Keywords: evolution equations; fractional stochastic; approximate controllability; equations nonlocal ... See more keywords
Existence of asymptotically periodic solutions for semilinear evolution equations with nonlocal initial conditions
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DOI: 10.1515/math-2018-0068
Abstract: Abstract In this paper we study a class of semilinear evolution equations with nonlocal initial conditions and give some new results on the existence of asymptotically periodic mild solutions. As one would expect, the results… read more here.
Keywords: semilinear evolution; nonlocal initial; evolution equations; initial conditions ... See more keywords
Fractional Langevin Equations with Nonlocal Integral Boundary Conditions
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DOI: 10.3390/math7050402
Abstract: In this paper, we investigate a class of nonlinear Langevin equations involving two fractional orders with nonlocal integral and three-point boundary conditions. Using the Banach contraction principle, Krasnoselskii’s and the nonlinear alternative Leray Schauder theorems,… read more here.
Keywords: fractional langevin; integral boundary; equations nonlocal; boundary conditions ... See more keywords