The supplementation of the theory of periodic solutions for a class of nonlinear diffusion equations

Huang, Haochuan; Huang, Rui; Yin, Jingxue

doi:10.1016/j.amc.2018.10.070

Cited by 2 publications

(3 citation statements)

References 9 publications

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“… If

p = 2, m = 1

, then

\frac{q}{m} = p - 1

becomes

q = 1

, and

\frac{q}{m} = q_{s}

becomes q = p s , which are the singular exponent and critical exponent respectively for Lane–Emden type equation, see previous works 11–13 If

p = 2

, then

\frac{q}{m} = p - 1

becomes

\frac{q}{m} = 1

, and

\frac{q}{m} = q_{s}

becomes

\frac{q}{m} = p_{s}

, which are the singular exponent and critical exponent respectively for porous medium equation, see our recent work 14 The above results can be summarized in the following table.…”

Section: Preliminaries and The Main Resultsmentioning

confidence: 64%

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Singular curve and critical curve for doubly nonlinear Lane–Emden type equations

Huang

Yin

2021

Math Methods in App Sciences

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“… If

p = 2, m = 1

, then

\frac{q}{m} = p - 1

becomes

q = 1

, and

\frac{q}{m} = q_{s}

becomes q = p s , which are the singular exponent and critical exponent respectively for Lane–Emden type equation, see previous works 11–13 If

p = 2

, then

\frac{q}{m} = p - 1

becomes

\frac{q}{m} = 1

, and

\frac{q}{m} = q_{s}

becomes

\frac{q}{m} = p_{s}

, which are the singular exponent and critical exponent respectively for porous medium equation, see our recent work 14 The above results can be summarized in the following table.…”

Section: Preliminaries and The Main Resultsmentioning

confidence: 64%

“…If

p = 2

, then

\frac{q}{m} = p - 1

becomes

\frac{q}{m} = 1

, and

\frac{q}{m} = q_{s}

becomes

\frac{q}{m} = p_{s}

, which are the singular exponent and critical exponent respectively for porous medium equation, see our recent work 14 …”

Section: Preliminaries and The Main Resultsmentioning

confidence: 88%

Singular curve and critical curve for doubly nonlinear Lane–Emden type equations

Huang

Yin

2021

Math Methods in App Sciences

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“…For these reasons, some scholars have studied the existence of periodic solutions of integer-order diffusion equations. [14][15][16] Thus, the problem that the existence of periodic solutions to fractional diffusion equations is the same as that of integer-order diffusion equations or not is worth studying. Let us note the difference between the integer derivatives and fractional derivatives of periodic functions, 17-19R…”

mentioning

confidence: 99%

Existence of periodic and S‐asymptotically periodic solutions to fractional diffusion equations with analytic semigroups

Nan

Zhou

2019

Math Methods in App Sciences

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In this paper, we study periodic and S‐asymptotically periodic solutions for fractional diffusion equations (FDE). As we all know, there is no exact periodic solution to differential equations with Caputo or Riemann‐Liouville fractional derivatives. Even so, in this paper, periodic (S‐asymptotically periodic) mild or classical solutions for FDE with Weyl‐Liouville fractional derivatives could be obtained in various fractional power spaces. In addition, a numerical simulation example and a specific example of fractional diffusion equation are given to verify the main theoretical results.

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The supplementation of the theory of periodic solutions for a class of nonlinear diffusion equations

Cited by 2 publications

References 9 publications

Singular curve and critical curve for doubly nonlinear Lane–Emden type equations

Singular curve and critical curve for doubly nonlinear Lane–Emden type equations

Existence of periodic and S‐asymptotically periodic solutions to fractional diffusion equations with analytic semigroups

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