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
Existence Results to a Class of Nonlinear Parabolic Systems Involving Potential and Gradient Terms
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DOI: 10.1007/s00009-020-01542-2
Abstract: In this paper, we investigate the existence of solutions to a nonlinear parabolic system, which couples a non-homogeneous reaction-diffusion-type equation and a non-homogeneous viscous Hamilton–Jacobi one. The initial data and right-hand sides satisfy suitable integrability… read more here.
Keywords: parabolic systems; results class; systems involving; class nonlinear ... See more keywords
Partial Regularity for Type Two Doubly Nonlinear Parabolic Systems
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DOI: 10.1007/s00205-018-1286-5
Abstract: We consider weak solutions v : $${U \times (0, T ) \rightarrow \mathbb{R}^{m}}$$U×(0,T)→Rm of the nonlinear parabolic system $${D\psi({v}_{t} ) = {\rm div} DF({D}_{v}),}$$Dψ(vt)=divDF(Dv), where $${\psi}$$ψ and F are convex functions. This is a prototype… read more here.
Keywords: regularity type; partial regularity; nonlinear parabolic; doubly nonlinear ... See more keywords
Linearly implicit BDF methods for nonlinear parabolic interface problems
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DOI: 10.1007/s10543-016-0641-x
Abstract: We analyze linearly implicit BDF methods for the time discretization of a nonlinear parabolic interface problem, where the computational domain is divided into two subdomains by an interface, and the nonlinear diffusion coefficient is discontinuous… read more here.
Keywords: implicit bdf; nonlinear parabolic; bdf methods; linearly implicit ... See more keywords
Blowing Up Solutions for Nonlinear Parabolic Systems with Unequal Elliptic Operators
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DOI: 10.1007/s10884-019-09790-x
Abstract: We give sufficient conditions for the boundedness of the blow-up set and no boundary blow-up for type I blowing up solutions to a nonlinear parabolic system with unequal elliptic operators. We introduce a new method… read more here.
Keywords: solutions nonlinear; blowing solutions; parabolic systems; nonlinear parabolic ... See more keywords
Convergence of a Second-Order Linearized BDF–IPDG for Nonlinear Parabolic Equations with Discontinuous Coefficients
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DOI: 10.1007/s10915-016-0261-2
Abstract: We study the anti-symmetric interior over-penalized discontinuous Galerkin finite element methods for solving nonlinear parabolic interface problems with second-order backward difference formula for the time discretization, where the diffusion coefficient depends on the unknown solution… read more here.
Keywords: order; second order; nonlinear parabolic; convergence second ... See more keywords
Vertex-Centered Linearity-Preserving Schemes for Nonlinear Parabolic Problems on Polygonal Grids
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DOI: 10.1007/s10915-016-0309-3
Abstract: On arbitrary polygonal grids, a family of vertex-centered finite volume schemes are suggested for the numerical solution of the strongly nonlinear parabolic equations arising in radiation hydrodynamics and magnetohydrodynamics. We define the primary unknowns at… read more here.
Keywords: vertex centered; linearity preserving; nonlinear parabolic; parabolic problems ... See more keywords
Local subestimates of solutions to double-phase parabolic equations via nonlinear parabolic potentials
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DOI: 10.1007/s10958-019-04515-3
Abstract: For parabolic equations with nonstandard growth conditions, we prove local boundedness of weak solutions in terms of nonlinear parabolic potentials of the right-hand side of the equation. read more here.
Keywords: parabolic potentials; subestimates solutions; local subestimates; nonlinear parabolic ... See more keywords
Renormalized solutions to nonlinear parabolic problems with blowing up coefficients and general measure data
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DOI: 10.1007/s11587-019-00436-0
Abstract: An existence result is established for a class of quasilinear parabolic problem which is a diffusion type equations having continuous coefficients blowing up for a finite value of the unknown, a second hand $$\mu \in… read more here.
Keywords: solutions nonlinear; nonlinear parabolic; parabolic problems; renormalized solutions ... See more keywords
Rothe time-discretization method for a nonlinear parabolic p(u) -Laplacian problem with Fourier-type boundary condition and $$L^1$$-data
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DOI: 10.1007/s11587-020-00544-2
Abstract: In this paper, we prove the existence and uniqueness results of entropy solutions to a class of nonlinear parabolic p(u)-Laplacian problem with Fourier-type boundary conditions and $$L^1$$ -data. The main tool used here is the… read more here.
Keywords: fourier type; problem fourier; type boundary; nonlinear parabolic ... See more keywords
Existence result of entropy solution for some nonlinear parabolic problems under natural growths in Musielak spaces
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DOI: 10.1007/s11587-021-00591-3
Abstract: In this article, we deal with the existence result for nonlinear parabolic equations of the form $$\begin{aligned} \frac{\partial u}{\partial t}-{\text {div}}\>\mathcal {A}(x,t,u,\nabla u)-\hbox {div}\Phi (x,t,u)= f \quad \text {in }{\Omega _T=\Omega \times (0,T)}, \end{aligned}$$ with… read more here.
Keywords: existence result; nonlinear parabolic; entropy solution; result entropy ... See more keywords