Addressing Complex Boundary Conditions of Miscible Flow and Transport in Two and Three Dimensions with Application to Optimal Control: Addressing complex boundary conditions of miscible flow and transport in two and three dimensions with application to optimal control

Authors: Yiqun Li, Hong Wang, Xiangcheng Zheng

Source: SIAM Journal on Applied Mathematics. 85:896-915

Subject Terms: 35K20, 49J20, 49K20, 76S05, advection-diffusion, diffusion-dispersion tensor, Flows in porous media, filtration, seepage, Existence theories for optimal control problems involving partial differential equations, PDEs in connection with fluid mechanics, boundary condition, optimal control, Optimization and Control (math.OC), Initial-boundary value problems for second-order parabolic equations, miscible displacement system, FOS: Mathematics, Optimality conditions for problems involving partial differential equations, Mathematics - Optimization and Control

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Access URL: http://arxiv.org/abs/2403.14079
https://zbmath.org/8035699
https://doi.org/10.1137/24m1647990

The Calderón problem for a nonlocal diffusion equation with time-dependent coefficients

Authors: Yi-Hsuan Lin, Jesse Railo, Philipp Zimmermann

Source: Revista Matemática Iberoamericana. 41:1129-1172

Subject Terms: Inverse problems for PDEs, Calderón problem, conductivity equation, fractional gradient, Fractional partial differential equations, Functional Analysis (math.FA), Mathematics - Functional Analysis, Mathematics - Analysis of PDEs, Fractional derivatives and integrals, Initial-boundary value problems for second-order parabolic equations, FOS: Mathematics, nonlocal Neumann derivative, fractional Laplacian, Runge approximation, Primary 35R30, secondary 26A33, 42B37, Liouville reduction, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2211.07781

On the solvability of an inverse problem for the Burgers equation with an integral overdetermination condition in a nonlinearly degenerating domain

Authors: Muvasharkhan T. Jenaliyev, Sergey I. Kabanikhin, Medina Kassen, Madi G. Yergaliyev

Source: Journal of Inverse and Ill-posed Problems. 33:93-106

Subject Terms: Inverse problems for PDEs, non-parabolic domain, Initial-boundary value problems for second-order parabolic equations, integral overdetermination condition, Nonlinear parabolic equations, Moving boundary problems for PDEs, inverse problem, Burgers equation, periodic boundary condition

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Access URL: https://zbmath.org/7984162
https://doi.org/10.1515/jiip-2024-0067

Blow-up and Decay of Global Solutions for a Free Boundary Problem with Competing Nonlocal Nonlinearity and Absorption: Blow-up and decay of global solutions for a free boundary problem with competing nonlocal nonlinearity and absorption

Authors: Hoang Huy Truong, Dung Tien Nguyen, Hoang-Hung Vo

Source: Acta Mathematica Vietnamica. 50:1-31

Subject Terms: Integro-partial differential equations, global slow solution, Initial-boundary value problems for second-order parabolic equations, Free boundary problems for PDEs, parabolic system, Integro-differential operators, Semilinear parabolic equations, global fast solution, free boundary, blow-up, Maximum principles in context of PDEs

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Boundary Riesz potential estimates for parabolic equations with measurable nonlinearities

Authors: Lee, Ho-Sik, Kim, Youchan

Source: Communications in Analysis and Mechanics, Vol 17, Iss 1, Pp 61-99 (2025)

Subject Terms: riesz potentials, measurable nonlinearities, PDEs with low regular coefficients and/or low regular data, Riesz potentials, Smoothness and regularity of solutions to PDEs, Initial-boundary value problems for second-order parabolic equations, QA801-939, nonlinear parabolic equations, Analytic mechanics, Nonlinear parabolic equations, PDEs with measure, A priori estimates in context of PDEs, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

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Access URL: https://doaj.org/article/753a5937591c43ea822c8d162ecba479

Inverse Problem of Determining the Absorption Coefficient in a Multidimensional Nonuniformly Parabolic Equation: Inverse problem of determining the absorption coefficient in a multidimensional nonuniformly parabolic equation

Authors: Kamynin, V. L.

Source: Mathematical Notes. 116:975-986

Subject Terms: Inverse problems for PDEs, Initial-boundary value problems for second-order parabolic equations, integral observation, nonuniformly parabolic equations, inverse problems of determining lowest coefficient

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Access URL: https://zbmath.org/8026301
https://doi.org/10.1134/s0001434624110105

Local Modification of Subdiffusion by Initial Fickian Diffusion: Multiscale Modeling, Analysis, and Computation: Local modification of subdiffusion by initial Fickian diffusion: multiscale modeling, analysis, and computation

Authors: Zheng, Xiangcheng, Li, Yiqun, Qiu, Wenlin

Source: Multiscale Modeling & Simulation. 22:1534-1557

Subject Terms: variable exponent, subdiffusion, Initial-boundary value problems for second-order parabolic equations, multiscale diffusion, error estimate, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, 35R11, 65M12, Fractional partial differential equations, well-posedness and regularity

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Access URL: http://arxiv.org/abs/2401.16885

On the Regularity Problem for Parabolic Operators and the Role of Half-Time Derivative: On the regularity problem for parabolic operators and the role of half-time derivative

Authors: Martin Dindoš

Source: J Geom Anal

Subject Terms: Mathematics - Analysis of PDEs, parabolic PDEs, boundary value problems, half-derivative, Smoothness and regularity of solutions to PDEs, Initial-boundary value problems for second-order parabolic equations, FOS: Mathematics, Initial-boundary value problems for second-order parabolic systems, Second-order parabolic systems, 35K10, 35K20, 35K40, 35K51, non-tangential maximal function, Article, Analysis of PDEs (math.AP)

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Access URL: https://pubmed.ncbi.nlm.nih.gov/40191766
http://arxiv.org/abs/2308.12936
https://zbmath.org/8029587
https://doi.org/10.1007/s12220-025-01991-9

Multidomain Hybrid Direct DG and Central Difference Methods for Viscous Terms in Hyperbolic-Parabolic Equations: Multidomain hybrid direct DG and central difference methods for viscous terms in hyperbolic-parabolic equations

Authors: Yuan, Weixiong, Liu, Tiegang, Zhang, Bin, Cao, Kui, Wang, Kun

Source: Numerical Mathematics: Theory, Methods and Applications. 17:1-36

Subject Terms: central difference schemes, hyperbolic-parabolic equations, Hyperbolic conservation laws, Initial-boundary value problems for second-order parabolic equations, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, viscous terms, Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems, direct discontinuous Galerkin, multidomain hybrid methods

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Improved Scalar Auxiliary Variable Schemes for Original Energy Stability of Gradient Flows: Improved scalar auxiliary variable schemes for original energy stability of gradient flows

Authors: Rui Chen, Tingfeng Wang, Xiaofei Zhao

Source: Journal of Scientific Computing. 103

Subject Terms: convergence, Applications to the sciences, Initial-boundary value problems for second-order parabolic equations, gradient flows, Allen-Cahn and Cahn-Hilliard equations, improved scalar auxiliary variable scheme, FOS: Mathematics, Nonlinear parabolic equations, Initial-boundary value problems for higher-order parabolic equations, original energy stability, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

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Access URL: http://arxiv.org/abs/2405.03403
https://zbmath.org/8018369
https://doi.org/10.1007/s10915-025-02796-2

On determining the fractional exponent of the subdiffusion equation

Authors: Shavkat Alimov, Ravshan Ashurov

Source: Journal of Inverse and Ill-posed Problems.

Subject Terms: Inverse problems for PDEs, Mathematics - Analysis of PDEs, Initial-boundary value problems for second-order parabolic equations, the Riemann-Liouville fractional derivative, FOS: Mathematics, subdiffusion equation, inverse problem, Fractional partial differential equations, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2411.19852

On a Bistable Delayed Nonlinear Reaction–Diffusion Equation for a Two‐Phase Free Boundary: Semi‐Wave and Its Numerical Simulation: On a bistable delayed nonlinear reaction-diffusion equation for a two-phase free boundary: semi-wave and its numerical simulation

Authors: Thanh‐Hieu Nguyen

Source: Studies in Applied Mathematics. 154

Subject Terms: semi-wave, Reaction-diffusion equations, Initial-boundary value problems for second-order parabolic equations, Free boundary problems for PDEs, time delay, bistable equation, free boundary problem

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Access URL: https://zbmath.org/8008944
https://doi.org/10.1111/sapm.70024

Nonlinear heat equation with viscoelastic term: Global existence and blowup in finite time: Nonlinear heat equation with viscoelastic term: global existence and blowup in finite time

Authors: Vu Ngo Tran, Dung Dao Bao

Source: Demonstratio Mathematica, Vol 58, Iss 1, Pp 961-990 (2025)

Subject Terms: global existence, decay rate, blowup in finite time, 35b40, Asymptotic behavior of solutions to PDEs, 35k51, Blow-up in context of PDEs, Integro-partial differential equations, viscoelastic, Initial-boundary value problems for second-order parabolic equations, nonlinear heat equation, QA1-939, Semilinear parabolic equations, Mathematics

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Access URL: https://doaj.org/article/6d849b622dfe449e83ca8393a1e9c431

Existence and uniqueness for renormalized solutions to noncoercive nonlinear parabolic equations with unbounded convective term

Authors: Dang, Thi Tam, Orlandi, Giandomenico

Source: Rendiconti del Seminario Matematico della Università di Padova. 153:61-79

Subject Terms: noncoercive problems, Quasilinear parabolic equations, Lorentz spaces, Initial-boundary value problems for second-order parabolic equations, partial differential equations, nonlinear parabolic equations, renormalized solutions, Weak solutions to PDEs

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A higher order stable numerical approximation for time‐fractional non‐linear Kuramoto–Sivashinsky equation based on quintic B‐‐spline: A higher order stable numerical approximation for time-fractional non-linear Kuramoto-Sivashinsky equation based on quintic \(\mathfrak{B}\)-spline

Authors: Renu Choudhary, Satpal Singh, Pratibhamoy Das, Devendra Kumar

Source: Mathematical Methods in the Applied Sciences. 47:11953-11975

Subject Terms: convergence, L1-2 scheme, Nonlinear higher-order PDEs, stability analysis, Fractional partial differential equations, 01 natural sciences, Caputo derivative, time varying layer, L1 scheme, Burgers' equation, Initial-boundary value problems for second-order parabolic equations, 0101 mathematics, computational cost, higher order splines, time-fractional Kuramoto-Sivashinsky equation

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Initial-boundary value problems to the time-space nonlocal diffusion equation

Authors: Borikhanov, Meiirkhan B., Mambetov, Samat A.

Source: Fractional Differential Calculus. :101-108

Subject Terms: integral equation, time-space nonlocal diffusion equation, fractional derivatives, Heat equation, Initial-boundary value problems for second-order parabolic equations, the method of separation variables, Fractional partial differential equations

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Existence of Weak Solutions for a Volume-Filling Model of Cell Invasion into Extracellular Matrix: Existence of weak solutions for a volume-filling model of cell invasion into extracellular matrix

Authors: Rebecca M. Crossley, Jan-Frederik Pietschmann, Markus Schmidtchen

Source: Journal of Differential Equations. 428:721-746

Subject Terms: ddc:510, gradient flow, Quasilinear parabolic equations, Mathematics - Analysis of PDEs, Initial-boundary value problems for second-order parabolic equations, Cell movement (chemotaxis, etc.), weak solutions, existence, FOS: Mathematics, cross-diffusion, Weak solutions to PDEs, volume exclusion, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2407.11228
https://zbmath.org/8017157
https://doi.org/10.1016/j.jde.2025.02.023
https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-1192584
https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/119258
https://doi.org/10.1016/j.jde.2025.02.023
https://opus.bibliothek.uni-augsburg.de/opus4/files/119258/1-s2.0-S0022039625001421-main.pdf

Nonstationary Venttsel problems with discontinuous data

Authors: Darya E. Apushkinskaya, Alexander I. Nazarov, Dian K. Palagachev, Lubomira G. Softova

Source: Journal of Differential Equations. 375:538-566

Subject Terms: Quasilinear parabolic equations, PDEs with low regular coefficients and/or low regular data, 35K20, 35R05, 35K59, maximal regularity, Strong solutions to PDEs, parabolic, quasilinear, A priori estimates in context of PDEs, 01 natural sciences, Mathematics - Analysis of PDEs, Parabolic Venttsel problem, measurable coefficients, strong solutions, linear equations, quasilinear equations, Initial-boundary value problems for second-order parabolic equations, partially VMO, FOS: Mathematics, strong solvability, Venttsel problem, 0101 mathematics, Diffusion processes, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2211.09232

Global boundedness of solutions to a class of partial differential equations with time delay

Authors: Xuanyu Liu, Junping Shi, Chuncheng Wang, Dejun Fan

Source: Journal of Differential Equations. 435:113232

Subject Terms: entropy method, global boundedness, Reaction-diffusion equations, Initial-boundary value problems for second-order parabolic equations, reaction diffusion equations, memory effect, Weak solutions to PDEs, time delay, A priori estimates in context of PDEs

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Access URL: https://zbmath.org/8035403
https://doi.org/10.1016/j.jde.2025.113232

On the evolution problem for the non-parametric prescribed mean curvature equation

Authors: Maria Michaela Porzio, Giuseppe Riey

Source: Journal of Mathematical Analysis and Applications. 548:129420

Subject Terms: mean curvature problem, regularity properties, Smoothness and regularity of solutions to PDEs, Initial-boundary value problems for second-order parabolic equations, nonlinear parabolic equations, boundedness, dirichlet problem, Quasilinear parabolic equations with mean curvature operator, Dirichlet problem

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