Nodea-Nonlinear Differential Equations and Applications最新文献

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Existence and non-existence results for a semilinear fractional Neumann problem 一类半线性分数阶Neumann问题的存在性与不存在性结果

4区数学 Q2 MATHEMATICS, APPLIED

Nodea-Nonlinear Differential Equations and Applications

Pub Date : 2023-10-03 DOI: 10.1007/s00030-023-00886-4

Eleonora Cinti, Francesca Colasuonno

Abstract We establish a priori $$L^infty $$ L ∞ -estimates for non-negative solutions of a semilinear nonlocal Neumann problem. As a consequence of these estimates, we get non-existence of non-constant solutions under suitable assumptions on the diffusion coefficient and on the nonlinearity. Moreover, we prove an existence result for radial, radially non-decreasing solutions in the case of a possible supercritical nonlinearity, extending to the case $$0 0 < s ≤ 1 / 2 the analysis started in [7].

摘要建立了一类半线性非局部Neumann问题非负解的先验$$L^infty $$ L∞估计。根据这些估计，在适当的扩散系数和非线性假设下，我们得到了非常解的不存在性。此外，我们证明了在可能的超临界非线性情况下径向非递减解的存在性结果，并推广到$$0<sle 1/2$$ 0 ＆lt;S≤1 / 2，从[7]开始分析。

引用次数: 1

Nonlinear dynamic problems for 2D magnetoelastic waves 二维磁弹性波的非线性动力学问题

4区数学 Q2 MATHEMATICS, APPLIED

Nodea-Nonlinear Differential Equations and Applications

Pub Date : 2023-09-25 DOI: 10.1007/s00030-023-00887-3

Viatcheslav Priimenko, Mikhail Vishnevskii

引用次数: 0

Asymptotic mean value properties for the elliptic and parabolic double phase equations 椭圆型和抛物型双相方程的渐近均值性质

4区数学 Q2 MATHEMATICS, APPLIED

Nodea-Nonlinear Differential Equations and Applications

Pub Date : 2023-09-20 DOI: 10.1007/s00030-023-00884-6

Weili Meng, Chao Zhang

引用次数: 0

The bounded slope condition for parabolic equations with time-dependent integrands 具有时变积分的抛物型方程的有界斜率条件

4区数学 Q2 MATHEMATICS, APPLIED

Nodea-Nonlinear Differential Equations and Applications

Pub Date : 2023-09-12 DOI: 10.1007/s00030-023-00876-6

Leah Schätzler, Jarkko Siltakoski

Abstract In this paper, we study the Cauchy–Dirichlet problem $$begin{aligned} left{ begin{array}{ll} partial _t u - {text {div}} left( D_xi f(t, Du)right) = 0 &{} quad hbox {in} Omega _T, u = u_o &{} quad hbox { on} partial _{mathcal {P}} Omega _T, end{array} right. end{aligned}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtable> <mml:mtr> <mml:mtd> <mml:mfenced> <mml:mrow> <mml:mtable> <mml:mtr> <mml:mtd> <mml:mrow> <mml:msub> <mml:mi>∂</mml:mi> <mml:mi>t</mml:mi> </mml:msub> <mml:mi>u</mml:mi> <mml:mo>-</mml:mo> <mml:mtext>div</mml:mtext> <mml:mfenced> <mml:msub> <mml:mi>D</mml:mi> <mml:mi>ξ</mml:mi> </mml:msub> <mml:mi>f</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>,</mml:mo> <mml:mi>D</mml:mi> <mml:mi>u</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mfenced> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:mtd> <mml:mtd> <mml:mrow> <mml:mrow /> <mml:mspace /> <mml:mtext>in</mml:mtext> <mml:mspace /> <mml:msub> <mml:mi>Ω</mml:mi> <mml:mi>T</mml:mi> </mml:msub> <mml:mo>,</mml:mo> </mml:mrow> </mml:mtd> </mml:mtr> <mml:mtr> <mml:mtd> <mml:mrow> <mml:mrow /> <mml:mi>u</mml:mi> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>u</mml:mi> <mml:mi>o</mml:mi> </mml:msub> </mml:mrow> </mml:mtd> <mml:mtd> <mml:mrow> <mml:mrow /> <mml:mspace /> <mml:mspace /> <mml:mtext>on</mml:mtext> <mml:mspace /> <mml:msub> <mml:mi>∂</mml:mi> <mml:mi>P</mml:mi> </mml:msub> <mml:msub> <mml:mi>Ω</mml:mi> <mml:mi>T</mml:mi> </mml:msub> <mml:mo>,</mml:mo> </mml:mrow> </mml:mtd> </mml:mtr> </mml:mtable> </mml:mrow> </mml:mfenced> </mml:mtd> </mml:mtr> </mml:mtable> </mml:mrow> </mml:math> where $$Omega subset mathbb {R}^n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Ω</mml:mi> <mml:mo>⊂</mml:mo> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> </mml:math> is a convex and bounded domain, $$f:[0,T]times {mathbb {R}}^n rightarrow {mathbb {R}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>:</mml:mo> <mml:mrow> <mml:mo>[</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mi>T</mml:mi> <mml:mo>]</mml:mo> </mml:mrow> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> <mml:mo>→</mml:mo> <mml:mi>R</mml:mi> </mml:mrow> </mml:math> is $$L^1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:math> -integrable in time and convex in the second variable. Assuming that the initial and boundary datum $$u_o:{overline{Omega }}rightarrow {mathbb {R}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>u</mml:mi> <mml:mi>o</mml:mi> </mml:msub> <mml:mo>:</mml:mo> <mml:mover> <mml:mi>Ω</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mo>→</mml:mo> <mml:mi>R</mml:mi> </mml:mrow> </mml:math> satisfies the bounded slope condition, we prove the exis

摘要本文研究了柯西-狄利克雷问题$$begin{aligned} left{ begin{array}{ll} partial _t u - {text {div}} left( D_xi f(t, Du)right) = 0 &{} quad hbox {in} Omega _T, u = u_o &{} quad hbox { on} partial _{mathcal {P}} Omega _T, end{array} right. end{aligned}$$∂tu - div D ξ f (t, du)在Ω t上= 0，在∂P Ω t上u = u o，其中$$Omega subset mathbb {R}^n$$ Ω∧R n是一个凸有界定域，$$f:[0,T]times {mathbb {R}}^n rightarrow {mathbb {R}}$$ f: [0, t] × R n→R是$$L^1$$ L 1 -在时间上可积，在第二变量上是凸的。假设初始和边界基准$$u_o:{overline{Omega }}rightarrow {mathbb {R}}$$ uo: Ω¯→R满足有界斜率条件，证明了在空间变量上存在唯一的Lipschitz连续变分解。

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引用次数: 0

The Brezis–Nirenberg problem for systems involving divergence-form operators 涉及散度形式算子的系统的Brezis-Nirenberg问题