Nonnegative solutions to reaction–diffusion system with cross‐diffusion and nonstandard growth conditions
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DOI: 10.1002/mma.6401
Abstract: We establish the existence of nonnegative weak solutions to nonlinear reaction–diffusion system with cross‐diffusion and nonstandard growth conditions subject to the homogeneous Neumann boundary conditions. We assume that the diffusion operators satisfy certain monotonicity condition… read more here.
Keywords: nonstandard growth; diffusion; diffusion system; growth conditions ... See more keywords
Recent developments in problems with nonstandard growth and nonuniform ellipticity
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DOI: 10.1016/j.jmaa.2021.125197
Abstract: Article history: Available online 26 March 2021 Submitted by G. Chen read more here.
Keywords: recent developments; nonstandard growth; problems nonstandard; developments problems ... See more keywords
Pullback exponential attractors for second-order lattice system with nonstandard growth condition
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DOI: 10.1063/5.0117249
Abstract: In this paper, we study the existence of pullback attractors and pullback exponential attractors for lattice dynamical system in time-dependent sequence space. First, we introduce a new sequence space with time-dependent variable exponents. Second, two… read more here.
Keywords: system; nonstandard growth; exponential attractors; lattice ... See more keywords
Inverse Problem for an Equation with A Nonstandard Growth Condition
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DOI: 10.1134/s0021894419020081
Abstract: This paper describes an inverse problem for determining the right side of a parabolic equation with a nonstandard growth condition and integral overdetermination condition. The Galerkin method is used to prove the existence of two… read more here.
Keywords: nonstandard growth; problem; equation nonstandard; growth condition ... See more keywords
On Solutions of a Parabolic Equation with Nonstandard Growth Condition
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DOI: 10.1155/2020/9397620
Abstract: A parabolic equation with nonstandard growth condition is considered. A kind of weak solution and a kind of strong solution are introduced, respectively; the existence of solutions is proved by a parabolically regularized method. The… read more here.
Keywords: equation nonstandard; parabolic equation; nonstandard growth; condition ... See more keywords
An optimization problem with volume constraint for an inhomogeneous operator with nonstandard growth
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DOI: 10.3934/dcds.2020391
Abstract: We consider an optimization problem with volume constraint for an energy functional associated to an inhomogeneous operator with nonstandard growth. By studying an auxiliary penalized problem, we prove existence and regularity of solution to the… read more here.
Keywords: nonstandard growth; optimization problem; problem; operator nonstandard ... See more keywords