New blow‐up conditions to p‐Laplace type nonlinear parabolic equations under nonlinear boundary conditions
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DOI: 10.1002/mma.7172
Abstract: In this paper, we study blow‐up phenomena of the following p‐Laplace type nonlinear parabolic equations ut=∇·ρ(|∇u|p)|∇u|p−2∇u+f(x,t,u),inΩ×(0,t∗), under nonlinear mixed boundary conditions ρ(|∇u|p)|∇u|p−2∂u∂n+θ(z)ρ(|u|p)|u|p−2u=h(z,t,u),onΓ1×(0,t∗), and u=0 on Γ2 × (0, t∗) such that Γ1∪Γ2=∂Ω , where f and h are… read more here.
Keywords: parabolic equations; boundary conditions; type nonlinear; laplace type ... See more keywords
Asymptotic output tracking for a class of semilinear parabolic equations: A semianalytical approach
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DOI: 10.1002/rnc.4504
Abstract: This paper addresses the problem of asymptotic output tracking of a class of semilinear parabolic equations with pointwise in‐domain actuation. First, the assessment of the well‐posedness of the considered systems is performed, and then, the… read more here.
Keywords: parabolic equations; tracking class; class semilinear; output tracking ... See more keywords
Discrete maximal regularity and the finite element method for parabolic equations
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DOI: 10.1007/s00211-017-0929-z
Abstract: Maximal regularity is a fundamental concept in the theory of partial differential equations. In this paper, we establish a fully discrete version of maximal regularity for parabolic equations on a polygonal or polyhedral domain $$\varOmega… read more here.
Keywords: finite element; maximal regularity; parabolic equations; method ... See more keywords
Numerical analysis of quasilinear parabolic equations under low regularity assumptions
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DOI: 10.1007/s00211-019-01071-5
Abstract: In this paper, we carry out the numerical analysis of a class of quasilinear parabolic equations, where the diffusion coefficient depends on the solution of the partial differential equation. The goal is to prove error… read more here.
Keywords: numerical analysis; analysis; quasilinear parabolic; parabolic equations ... See more keywords
Global Existence and Blow-up in Finite Time for a Class of Finitely Degenerate Semilinear Pseudo-parabolic Equations
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DOI: 10.1007/s10114-019-8037-x
Abstract: In this paper, we study the initial-boundary value problem for the semilinear pseudo-parabolic equations ut − ΔXut − ΔXu = |u|p−1u, where X = (X1,X2,…,Xm) is a system of real smooth vector fields which satisfy… read more here.
Keywords: time; finitely degenerate; pseudo parabolic; parabolic equations ... See more keywords
ℒ-Splines and Viscosity Limits for Well-Balanced Schemes Acting on Linear Parabolic Equations
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DOI: 10.1007/s10440-017-0122-5
Abstract: Well-balanced schemes, nowadays mostly developed for both hyperbolic and kinetic equations, are extended in order to handle linear parabolic equations, too. By considering the variational solution of the resulting stationary boundary-value problem, a simple criterion… read more here.
Keywords: balanced schemes; splines viscosity; linear parabolic; parabolic equations ... See more keywords
Control of Stackelberg for Coupled Parabolic Equations
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DOI: 10.1007/s10883-016-9354-3
Abstract: We consider the Stackelberg problem for coupled parabolic equations with a finite number of constraints on one of the states. This notion assumes that we have two controls to determine. The first control is supposed… read more here.
Keywords: control stackelberg; control; parabolic equations; coupled parabolic ... See more keywords
Convergence in the Hölder Space of the Solutions to Problems for Parabolic Equations with Two Small Parameters in Boundary Condition
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DOI: 10.1007/s10958-018-4119-z
Abstract: Multidimensional two-phase problem for the parabolic equations with two small parameters ε > 0 and κ > 0 at the leading terms in the conjugation condition is studied in the Hölder space. An estimate of… read more here.
Keywords: condition; two small; lder space; small parameters ... See more keywords
Inverse Source and Coefficient Problems for Elliptic and Parabolic Equations in Hölder and Sobolev Spaces
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DOI: 10.1007/s10958-019-04184-2
Abstract: We review some results obtained by the authors during the last 15 years. In particular, we present the existence and uniqueness theorems for linear and nonlinear inverse problems of reconstructing unknown coefficients in elliptic and… read more here.
Keywords: elliptic parabolic; source coefficient; problems elliptic; inverse source ... See more keywords
On Coercive Solvability of Parabolic Equations with Variable Operators
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DOI: 10.1007/s10958-019-04321-x
Abstract: AbstractIn a Banach space E, the Cauchy problem υ′t+Atυt=ft0≤t≤1,υ0=υ0,$$ \upsilon^{\prime }(t)+A(t)\upsilon (t)=f(t)\kern1em \left(0\le t\le 1\right),\kern1em \upsilon (0)={\upsilon}_0, $$ is considered for a differential equation with linear strongly positive operator A(t) such that its domain D… read more here.
Keywords: variable operators; coercive solvability; equations variable; solvability ... See more keywords
Quasilinear parabolic equations with a degenerate absorption potential
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DOI: 10.1007/s10958-019-04489-2
Abstract: Quasilinear parabolic equations with a degenerate absorption potential are considered. The estimates of all weak solutions of such equations, including large solutions satisfying the blow-up conditions on the parabolic boundary of a domain, are obtained. read more here.
Keywords: quasilinear parabolic; absorption potential; degenerate absorption; parabolic equations ... See more keywords